Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
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Sobia Sultana
Abstract
Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.
1 Introduction
Chaotic systems are extremely responsive to initial conditions (ICs). The phenomenon is frequently referred to as the butterfly influence [1]. Chaos synchronization has garnered a lot of consideration in scientific circles since Pecora and Carroll [2] developed the notion of chaotic synchronization under various ICs. The concept behind synchronization is to take advantage of the data generated by the centralized system to regulate the slave mechanism and guarantee its results adhere to the production of the acquire mechanism asymptotically. One of the most crucial uses of chaos is the synchronization of multiple chaotic dynamical structures. Over recent decades, chaotic synchronization has emerged as an intriguing topic within the arena of scientific disciplines owing to its broad range of conceivable uses in fields including chemical processes, circuit theory, aeronautical engineering, image processing, photonics, optics, cyber security, electromagnetic flux, elasticity, and fluid systems [3]. For tackling the synchronization of alike or non-similar master-slave chaotic structures, many techniques are being developed, including active supervision techniques, adaptable control approaches, fuzzy oversight procedures, back-stepping design techniques, impulsively regulation approaches, automatic control processes, parametric feedback controlling techniques, and many more [4,5].
Whenever the settings are unidentified or change over time, adaptive synchronization is used to synchronize the same or non-identical mechanisms. Wang et al. [6] investigated responsive synchronization for a Chen chaotic structure via entirely unresolved factors. Lin et al. [7] contemplated the dynamic, powerful observer-based synchronization of unilaterally complemented chaotic networks with an unidentified transmit time delay. Fan et al. [8] presented synchronization of a family of chaotic systems based on adaptive control design of input-to-state stability. Chen et al. [9] expounded the hidden extreme multistability and synchronicity of memristor-coupled non-autonomous memristive Fitzhugh–Nagumo models.
Spacecraft emergence display was recently recognized as an enabler electronic device for numerous subsequent years of missions into outer space [3,4]. This system provides multiple positive effects over an individual rocket task, involving the capacity to boost and/or facilitate outreach by means of deeper starting point assessments, a high rate of failure tolerance, real-time reconfigurability, adaptability to extremely fluctuating requirements, and lesser lifetime expenses [10]. Nevertheless, from spacecraft formation setup to transformation, interaction, and pattern generation, the entire process presents enormous obstacles [11]. For deeper patterns, spacecraft substance, dominance, energy, and interactions pose substantial barriers and orientation, transportation, and operational obligations become exceedingly complex [12–14]. Environmental perturbations resulting from the force of gravity disruption, ambient drag, ultraviolet (UV) stress, and electromagnetism may cause the spacecraft to takeoff [15]. To address these issues, novel techniques for accomplishing spacecraft creation constellations while minimizing location maintenance necessities are being requested. The manoeuvring of spacecrafts in their navigation is critical to security forces, courteousness, and research endeavours. Spacecraft framework synchronization is an active academic field [16,17]. Several methods and procedures were implemented to synchronize and regulate non-linear phenomena (spacecraft attitude), specifically responsive oversight, proactive surveillance, and control using sliding mode [18,19]. The adaptable synchronization of spacecraft behaviour and momentum-based systems are complicated topics. The spacecraft behaviour framework includes unpredictability and disruptions (both exterior and interior). It is a redundant torque structure. The disruptions in the outermost layer may encompass streamlined experiences, ultraviolet ray-compelled tensions, gravitation gradient forces, and electromagnetic instances, whereas internal fluctuations can embrace parameter unpredictability [20–22]. Spacecraft mechanism synchronization is currently employed in contemporary space-purpose theories featuring multiple spacecrafts constellations with details. This is addressed by the synchronization regulation system, which regulates the variation in oversights within spacecraft constellations. The objective is to determine the advanced version of adaptive synchronization that motivates spacecraft constellations asynchronously regarding identical briefings [23,24].
In the last century, discrete fractional (DF) calculus has grown up as an appealing study field that has sparked the fascination of researchers from multiple fields [25–32]. Their uses range from biological science to environmental science to practical scientific fields, providing useful understanding of contemporary issues [27,33]. In contrast to classical non-fractional networks, fractional platforms have proven their capacity to specify multifaceted chaotic events with more precision [34,35]. It highlights their distinctive features, such as persistent memory, transparency, and adaptability. There is currently an increase in the number of articles presented on this fascinating subject [36,37]. Pérez et al. [38] proposed fractional algorithms that take into account order as an indicator of space and time or additional factors. There are also processes for such fractional V–O formulations in [39–42]. Because variable-order (V–O) fractional differential equations are unable to be addressed precisely, establishing computational methods to resolve them is critical. Pérez et al. proposed a constant-order quantitative method combining fractional calculus and Lagrange polynomials in [38]. They generalized mathematical strategies for modelling V–O fractional differential operators regarding index, exponential, and Mittag–Leffler functions, employing the aforementioned technique [43–48].
Stability hypothesis is an extensive discipline in technology and other allied areas that studies the behaviour of dynamic structures in both linear and non-linear frameworks [49]. On the contrary, substantial advancement has been achieved concerning the stability methodology for fractional order difference equations in recent years [50]. Nonetheless, the comparable concept of a discrete-time fractional-order system continues to evolve in an intriguing manner. In addition to this, the different kinds of durability discussed for this sort of equipment are the infinite and finite stability investigated in [49,50] for discrete fractional-order difference models with non-linearities as well as time interruptions. Furthermore, You et al. [51] investigated Mittag–Leffler stability for fractional discrete-time systems using a fixed-point strategy. Pratap et al. [52] provided a class of fractional-order discrete-time complex-valued neural networks with temporal delays while addressing multiple stability specifications. In addition, Huang et al. [53] discuss the asynchronous stability of discrete fractional-order neural networks and offer a novel algorithm for V–O neural networks.
Numerous researchers have proposed innovative formulations of discrete-time fractional calculus that have stability properties and multiple empirical results [54,55]. In particular, Abdeljawad [56] discussed the delta and nabla Caputo fractional differences and dual identities. Abdeljawad [57] offered groundbreaking research that explored the various kernels for h-fractional differences and their fractional sums. As a consequence, this research has opened pathways for the formation of additional chaotic dynamics [57]. Abdeljawad [58] expounded the fractional difference operators with discrete generalized Mittag–Leffler kernels. Also, it investigates multiple influence methods and synchronization schemes constructed to synchronize the connections of various fractional discrete chaotic environments [59–65]. These research investigations revealed that the mechanism’s behaviour is greatly reliant on the fractional order picked out, highlighting its dynamic and convoluted form, making it an exciting area for research in the discipline of fractional approaches [66–72].
In fact, most former spacecraft model studies have concentrated on classical calculus. Unfortunately, the scientific investigation of discrete fractional spacecraft models is still insufficient, with little research devoted to investigating their behaviour and attributes. Tsui and Jones [73] explored the control of higher-dimensional chaos in spacecraft attitude control problem. Kuang et al. [74] expounded the chaotic attitude motion of spacecrafts under small perturbation torques. Furthermore, Kuang et al. [75] contemplated the chaotic dynamics of an asymmetrical gyrostat. Kong et al. [76] described the control of chaotic attitude motion of a perturbed spacecraft, while Kumar et al. [77] investigated controlling and synchronization of a fractional-order chaotic spacecraft model. The research emphasizes the framework’s challenging and diverse behaviour, emphasizing the importance of fractional aspects in the sophistication and adaptability of spacecraft models. A great deal of the prior study concentrated mainly on commensurate-order theories in continuous-time fractional-order models. Yet it seems that there is a substantial dearth of research regarding the influence of the incommensurate scenario on the fluidity of these models. Indeed, incommensurate order is a subset of a fractional-order structure defined by revealing the order for which the formula differs. As a result, the simulation’s liberty strengthens. This points to an unresolved issue in the discipline of discrete models, especially within the setting of incommensurate fractional systems. Recognizing the functioning and features of incommensurate fractional spacecrafts may provide significant discoveries and prospective uses in a wide range of fields, including neural structures, technology, artificial intelligence, viscosity, control research, cognitive behaviour, and numerous others [20,78,79]. As a result, additional inquiry and exploration on this subject are required to identify the distinctive features and conceivable advantages of incommensurate fractional spacecraft models. It is pertinent to mention that research on discrete models with V–O has yielded inadequate findings. Huang et al. [53] investigated a type of variable-order recurrent neural network under the Caputo h-discrete fractional operator using fixed-point techniques and Mittag–Leffler stability specifications.
Motivated by the prior argumentation, the goal of this article is to investigate and evaluate the dynamic practices of the discrete fractional spacecraft system, which includes variable exponents. By means of an amalgamation of quantitative and qualitative inspections, we execute an extensive review of the key features of this discrete fractional spacecraft model. Moreover, we have established the existence and uniqueness of the proposed model to verify its efficacy. We investigate the chaotic behaviour of spacecraft constellations using multiple techniques, including dissipativity, fixed points, Poincaré maps, and actuator faults. The suggested system’s dissipative nature (strange attractor) is defended. We acquire the proposed model’s fixed points, and at every fixed point, we notice that a single of the eigenvalues of the spacecraft system’s Jacobian matrix is non-negative, confirming the zone of instability. By using the oversight-control procedure, we determine the synchronization of two equivalent spacecraft constellations. These investigations provide fresh perspectives on the functioning of spacecraft networks. GPS systems, telecommunications, planet perception, and climate prediction, can all benefit from measurements. This shows the distinctiveness of our work.
The article is organized as follows: in Section 2, we outline the discrete fractional spacecraft system and provide key introductory notions concerning discrete fractional calculus. Section 3 presents a qualitative analysis of the system architecture, focusing on its facts, which is followed by an explanation of the configuration’s design specifications in the second section. The dissipativeness of the system, Lyapunov exponent calculation, and phase depictions aid in this inquiry. Section 4 explores the existence and uniqueness of the discrete fractional spacecraft model. Section 5 entails applying the commensurate and incommensurate orders to determine variability and verify the existence of chaotic patterns in the system. In Section 6, we developed the robust controller model technique and synchronization has developed in view of the master and slave systems. Section 7 ends the work by indicating potential research goals.
2 Preliminaries and model description
Here, the terminology for discrete fractional calculus is offered in this part, accompanied by the subsequent notations:
Definition 2.1
[80] For
where the rising mapping is defined as
Definition 2.2
[80] For
where
and
Definition 2.3
[80] For
Theorem 2.1
[81] Suppose that
where
Lemma 2.1
Suppose there is a
Proof
For the first step with, we have
Notice that
Setting
For all
Thus, we find
This completes the proof.□
Next, the rotational motion of the formula for a steadfast spacecraft [82] can be written as follows:
where
The differentiation of the entire momentum
where
Thus, vector product in (2.15) can be composed as the combination of the skew-symmetric cross product matrix
In view of (2.16), the rotational speed can be written in context of differential equations as follows:
Here,
The formula for a three-dimensional in the form of chaotic spacecraft mechanism is:
where
The spacecraft structure in all three planes has been reformulated as follows:
where the values of
Furthermore, we present the ABC-discrete fractional form of the spacecraft model (2.20) as follows:
with the aforesaid parameters and
3 Qualitative analysis of fractional spacecraft model
This section investigates the requirements for dynamical evaluations of the discrete fractional spacecraft model (2.21), including dissipativity of the system, fixed points, invariancy of the
3.1 Existence of dissipativeness
Here, the vector representation of (2.21) can be described as follows:
where
where
Assume that
Making the use of Liouville’s theorem, we have
Thus, the divergence of the spacecraft model (2.21) is expressed as follows:
In view of (3.3) and (3.4), we attain the fractional difference equation as follows:
The solution of (3.5) can be described as follows:
Thus, the volumes of the beginning points decreased by
Phase portraits for 3D and 2D for fractional-order spacecraft model (2.21) with fractional-order
3.2 Equilibrium points
To investigate the dynamics of (2.21), we initially obtain the equilibrium points. First, we described the following lemma, which is mainly due to Matignon [83].
Lemma 3.1
[83] Assume that there is a equilibrium point
To identify the fixed points, address the subsequent expressions in (2.21) equating to zero as follows:
The expression has the fixed points:
Therefore, the Jacobian matrix of the system (2.21) is defined as follows:
The expression (3.8) at
At
The expression (3.8) at
At
The expression (3.8) at
At
Analogously, at
Stabilized zone for fractional-order system.
3.3 The invariancy of
x
2
-axis
According to discrete fractional spacecraft model (2.21), it is worth mentioning that when
which yields
As a result, the
3.4 Maximum Lyapunov exponents (
Ω
max
)
Employing the system parameters for
4 Existence and uniqueness
Consider the following ABC-discrete fractional variable order system is presented as follows:
such that
where
where
Theorem 4.1
Suppose assumptions
Proof
In view of ABC-discrete fractional VO characterization, then a solution of (2.21) is
By implemented the following norm;
Therefore, (4.5) can be transformed into a fixed problem. Take into account the subsequent mapping:
where
For every pair of distinct mappings
which leads us to
Making the use of Lemma 2.1, we have
Analogously, we have
In view of supposition
Our next result is the stability analysis of the discrete fractional spacecraft model (2.21).
Definition 4.1
[84] For initial time of the discrete variable order spacecraft model (2.21) having nabla discrete Mittag–Leffler kernel is adjusted as
Theorem 4.2
Assume that the supposition
then (2.21) is uniformly stable.
Proof
Assume that
equivalently,
Considering assumption
Furthermore, applying assumption
Consequently, we have
Analogously, we can find
Thus, we determine that for any
5 Numerical experimentation for the proposed model
In the following part, the focus is on the novel investigation of how the discrete fractional spacecraft model (2.21) behaves. The evaluation will include both commensurate and incommensurate orders. We will use a variety of computational resources for displaying phase portraits and poincaré maps.
5.1 Commensurate V–O
In this section, we will elaborate on the various properties of the commensurate order for the discrete fractional spacecraft system (2.21). It is essential to comprehend that a commensurate-order fractional system consists of formulas with similar orders. To achieve this, we shall subsequently provide the numerical calculation, which originates from Theorem 4.1 and will be provided as follows:
Choosing
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with V–O
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with V–O
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with V–O
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with V–O
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with fractional-order
Presently, alongside
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with fractional-order
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with fractional-order
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with fractional-order
Phase portraits for 2D and 3D discrete fractional spacecraft model (5.1) with V–O
5.2 Incommensurate V–O
The interactions of the incommensurate-order discrete fractional spacecraft model are investigated in this part. Incommensurate V–O requires employing distinctive orders to feed every formula in the structure. The incommensurate-order form of discrete fractional spacecraft model is represented in the following manner:
In view of Theorem 4.1, we are able to convey a mathematical representation of the incommensurate-order discrete fractional spacecraft model (5.2) in the following manner:
We investigate the processes and distinctive features of this visualization for the purpose of comprehending their peculiar behaviour and investigating the consequences of using distinguished orders in the system’s dynamics equations. Figures 12, 13, 14, 15, 16 show various chaotic diagrams that show the behaviour of the incommensurate-order discrete fractional spacecraft model (5.3) as the value of
Phase portraits for 2D and 3D for discrete fractional spacecraft model (5.3) with V–O
Phase portraits for 2D and 3D for discrete fractional spacecraft model (5.3) with V–O
Phase portraits for 2D and 3D for discrete fractional spacecraft model (5.3) with V–O
Phase portraits for 2D and 3D for discrete fractional spacecraft model (5.3) with V–O
Phase portraits for 2D and 3D for discrete fractional spacecraft model (5.3) with V–O
Case I: Figure 14 shows the change with respect to
Poincaré maps for discrete fractional spacecraft model (5.3) for various V–Os as mentioned earlier.
Case II: The Poincaré illustrations are displayed for studying the fluctuating behaviours of the incommensurate-order discrete fractional spacecraft model (5.3) via
Case III:
Figure 16 depicts the chaotic diagram and the accompanying Poincaré map of the identified novel incommensurate-order discrete fractional spacecraft model (5.3) using the parameter
6 Robust controller model technique
The powerful intolerant fault control system approach to development is explained in the next part. This layout depicts the monitoring plan. The suggested mechanism rules consists of two components:
(A) an insignificant device
(B) an effective compensation
The insignificant control device is intended in fact for the altered insignificant mechanism; the reliable compensating device is built from second-level filtering to limit the impact of the corresponding interruption. The powerful control device
Let
where
Considering (6.1) and (6.2), then the spacecraft dynamic framework is subsequently expressed as follows:
Then, in (6.3), the perturbation-free insignificant mechanism can be retrieved mechanically by overlooking the reliable a compensator
where the matrices
In addition, the effective compensated
where
In consideration of this, the researchers determine to interpret the analogous disruption
In view of (6.5) and (6.6), the sturdy compensating device
Plugging (6.5) into (6.7), then the powerful devise can be expressed as follows:
where
After simplification, we have
Multiplying
Analogously, we can find
where
In addition, the following is the recommendations for determining the theoretical controller boosts
Case I: Take out the disturbance-free insignificant structure using (6.3), and then choose the default controller’s advantages
Case II: Choose an effective compensating device parameter specification
Case III: In view of control assumption, the regulation precisioness condition issatisfied, the regulation preciseness prerequisite, the sturdy a compensator value
Case IV: When the envisioned regulate exactness is unable to be obtained by simply adjusting the compensating setting
Remark 6.1
It is noted that the mechanism suggested in (6.1) does not necessitate any details about device error. Furthermore, the intended improvement of the mechanism
Remark 6.2
The insignificant framework can be streamlined using the nominative influence rules in (6.4) as
In addition, the genuine mechanism results
Bar graph containing energy factors and fractional order
Bar graph containing energy factors and fractional order
6.1 Synchronization
Nonlinear regulators for coordinating the fractional-order spacecraft model are described in the subsequent section. The synchronization procedure seeks to minimize the difference between the master and slave visualizations, which compels it to gravitate towards zero. The master system is the commensurate fractional-order spacecraft model, represented by (5.1), while the slave system is characterized in the following manner:
where
The fractional error scheme is described as follows:
The suggested regulation govern that creates this synchronization system is described in the following theorem.
Theorem 6.1
Under the supposition of (6.12) and (6.13):
where
Proof
Plugging the regulate principle (6.16) in the fractional error system (6.13), we find:
where
Since
Mathematical computations using MATLAB are used to verify the truthfulness of this outcome. The parameters used are
Error dynamics of (5.1) having
7 Conclusion
The spacecraft interacts with the plasma physics such as solar wind, magnetospheres, and ionospheres. Understanding plasma physics helps mitigate effects like spacecraft charging and drag in low-earth orbit. This article proposes a discrete fractional spacecraft model and investigates its behaviour with commensurate and incommensurate V–Os. The Poincaré map’s assessment revealed a variety of unpredictable features, pointing out its dynamic diversity. The distinguished behaviours of the identified discrete fractional spacecraft model have been studied for both commensurate and incommensurate V–Os using various approaches to inspection, including phase pictures and time-evolution plots. Furthermore, the system’s challenges have been determined employing the robust controller technique with the actuator faults. The results highlight the significant impact of the network setting and fractional exponents on the configurations of the discrete fractional spacecraft model. The numerical representations of such variables are crucial for influencing the structure and functioning of the framework, and fluctuations in their significance result in various paths as well as effects in the system’s state domain. Finally, the article suggests efficient oversight rules for ensuring the reliability and synchronization of the implemented system by manipulating its status to asynchronously tend to zero. The numerical analyses performed provide an extensive overview of the mechanism’s interactions and illustrate its fascinating and distinct behaviours, which have been crucial in investigating the consequences of fractional spacecraft models.
In the future, the emergency network will evolve in the patterns of intelligence, integration, popularization, inexpensiveness, and space–air–ground–sea integration. Thanks to the continual growth of finances and societies as a whole, the emergency communication network has been additionally enhanced, and novel technologies for networks have come into existence. This will help expedite the commencement of emergency rescue operations.
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Funding information: The author states no funding involved.
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Author contribution: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The author states no conflict of interest.
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Data availability statement: Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.
References
[1] Carroll TL, Pecora LM, Synchronization chaotic circuits. IEEE Trans CAS. 1999;I(38):435–46. Search in Google Scholar
[2] Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys Rev Lett. 1990:64;821–4. 10.1103/PhysRevLett.64.821Search in Google Scholar PubMed
[3] Djaouida S. Synchronization of a perturbed spacecraft attitude motion. Int J Mech Aerosp Ind Mechatron. Manuf Eng. 2014;8(4):734–8. Search in Google Scholar
[4] Guan P, Liu XJ, Liu JZ. Flexible spacecraft attitude control via sliding mode technique. In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain. 12–15 Dec, 2005. Search in Google Scholar
[5] Smale S. Differentiable dynamical systems. Bull Am Math Soc. 1967:73;747–817. 10.1090/S0002-9904-1967-11798-1Search in Google Scholar
[6] Wang YW, Guan ZH, Wen X. Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos Solit Fract. 2004;19:899–903. 10.1016/S0960-0779(03)00256-XSearch in Google Scholar
[7] Lin JS, Liao TL, Yan JJ, Yau HT. Synchronization of unidirectional coupled chaotic systems with unknown channel time-delay: adaptive robust observer-based approach. Chaos Solit Fract. 2005:26(3):971–8. 10.1016/j.chaos.2005.02.005Search in Google Scholar
[8] Fan Y, Wang W, Lin Y. Synchronization of a class of chaotic systems based on adaptive control design of input-to-state stability. Int J Innov Comput Inf Cont. 2015:11(3):803–14. Search in Google Scholar
[9] Chen M, Luo X, Suo Y, Xu Q, Wu H. Hidden extreme multistability and synchronicity of memristor-coupled non-autonomous memristive Fitzhugh-Nagumo models. Nonlin Dyn. 2023;111:7773–88. https://doi.org/10.1007/s11071-023-08235-x. Search in Google Scholar
[10] Duan GR, Yu HH. LMI in control systems analysis, design and applications. Boca Raton: CRC Press; 2013. Search in Google Scholar
[11] Hamidzadeh SM, Esmaelzadeh R. Control and synchronization chaotic spacecraft using active control. Int J Comp Appl. 2014;94(10). 10.5120/16380-5887Search in Google Scholar
[12] Tuai AP, Jones AJ, The control of higher dimensional chaos: comparative results for the chaotic spacecraft attitude control problem. Phys Nonlin Phenom. 2000;135(1–2):41–62. Search in Google Scholar
[13] Wei W, Wang J, Zuo M, Liu Z, Du J. Chaotic spacecraft attitude control by adaptive approach, Int. J. Control. 2014;87(6):1196–207. 10.1080/00207179.2013.872299Search in Google Scholar
[14] Köose E. Controller design by using non-linear control methods for spacecraft chaotic system. Electr Eng. 2017;99(2):763–73. 10.1007/s00202-016-0450-xSearch in Google Scholar
[15] Faramin M, Ataei M. Chaotic attitude analysis of a spacecraft via Lyapunov exponents and its robust nonlinear control subject to disturbances and uncertainties, Nonlin Dyn. 2016;83(1–2):361–74. 10.1007/s11071-015-2333-5Search in Google Scholar
[16] Farid Y, Moghaddam TV. Generalized projective synchronization of chaotic spacecrafts problem using linear matrix inequality. Int J Dyn Cont. 2014;2(4):577–86. 10.1007/s40435-014-0089-2Search in Google Scholar
[17] Du H, Li S. Attitude synchronization for flexible spacecraft with communication delays. IEEE Trans Automat Cont. 2016;61(11):3625–30. 10.1109/TAC.2016.2525933Search in Google Scholar
[18] Wu B, Wang D, Poh EK. Decentralized robust adaptive control for attitude synchronization under directed communication topology. J Guid Cont Dyn. 2011;34(4):1276–82. 10.2514/1.50189Search in Google Scholar
[19] Zhou N, Xia Y, Wang M, Fu M. Finite-time attitude control of multiple rigid spacecraft using terminal sliding mode. Int J Robust Nonlin Cont. 2015;25(12):1862–76. 10.1002/rnc.3182Search in Google Scholar
[20] MacKunis W, Dupree K, Bhasin S, Dixon WE. Adaptive neural network spacecraft attitude control in the presence of inertia and CMG actuator uncertainties. in: 2008 American Control Conference IEEE. 2008. p. 2975–80. 10.1109/ACC.2008.4586948Search in Google Scholar
[21] Show LL, Juang JC, Jan YW. An LMI-based nonlinear attitude control approach. IEEE Trans Cont Sys Tech. 2003;11(1):73–83. 10.1109/TCST.2002.806450Search in Google Scholar
[22] Zhang C, Chen Z, Wei C. Sliding mode disturbance observer-based backstepping control for a transport aircraft, Sci China Inf Sci. 2014;57(5):1–16. 10.1007/s11432-013-4787-8Search in Google Scholar
[23] Li HY, Hu YA. Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties. Commun Nonl Sci Numer Sim. 2011;16(10):3904–13. 10.1016/j.cnsns.2011.02.031Search in Google Scholar
[24] Cong B, Liu X, Chen Z. Backstepping based adaptive sliding mode control for spacecraft attitude maneuvers, Aero Sci Tech. 2013;30(1):1–7. 10.1016/j.ast.2013.05.005Search in Google Scholar
[25] Hilfer R, Applications of fractional calculus in physics. Singapore: World Scientific; 2000. 10.1142/9789812817747Search in Google Scholar
[26] Atici FM, Eloe P. Discrete fractional calculus with the nabla operator. Electron J Qual Theory Differ Equ. 2009;3:2009. 10.14232/ejqtde.2009.4.3Search in Google Scholar
[27] Anastassiou GA. Principles of delta fractional calculus on time scales and inequalities. Math Comput Mode. 2010;52:556–66. 10.1016/j.mcm.2010.03.055Search in Google Scholar
[28] Chu YM, Alzahrani T, Rashid S, Alhulayyil H, Rashidah W, Rehman S. Complex dynamical analysis of fractional differences Willamowski-Rössler chemical reaction model in time-scale analysis, Res Phy. 2023;54(6):107023. 10.1016/j.rinp.2023.107023Search in Google Scholar
[29] Xu C, Farman M. Qualitative and ulam-Hyres stability analysis of fractional order cancer-immune model. Chaos Solit Fract. 2023:177;114277. 10.1016/j.chaos.2023.114277Search in Google Scholar
[30] Chu YM, Alzahrani T, Rashid S, Rashidah W, Rehman S, Alkhatib M. An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses. Sci Rep. 2023;13(1). 10.1038/s41598-023-45227-8Search in Google Scholar PubMed PubMed Central
[31] Farman M, Shehzad A, Nisar KS, Hincal E, Akgúl A, Hassan AM. Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem. Sci Reports. 2023;13:22441. 10.1038/s41598-023-49806-7Search in Google Scholar PubMed PubMed Central
[32] Gafel HS, Rashid S, Elagan SK. Novel codynamics of the HIV-1/HTLV-I model involving humoral immune response and cellular outbreak: A new approach to probability density functions and fractional operators. AIMS Math. 2023;8(12):28246–79. 10.3934/math.20231446Search in Google Scholar
[33] Atangana A. Extension of rate of change concept: From local to nonlocal operators withapplications. Res Phys. 2021;19:103515. https://doi.org/10.1016/j.rinp.2020.1. Search in Google Scholar
[34] Atangana A, Gómez-Aguilar JF. Fractional derivatives with no-index law property: Application to chaos and statistics. Chaos Solit Fract. 2018;114:516–35. https://doi.org/10.1016/j.chaos.2018.07.033. Search in Google Scholar
[35] Jarad F, Abdeljawad T, Hammouch Z. On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative. Chaos Solit Fract. 2018;117:16–20. https://doi.org/10.1016/j.chaos.2018.10.006. Search in Google Scholar
[36] Atangana A, Araz SI. New concept in calculus: Piecewise differential and integral operators. Chaos Solit Fract. 2021;145:110638. https://doi.org/10.1016/j.chaos.2020.110638. Search in Google Scholar
[37] Atangana A, Araz SI. Deterministic-stochastic modeling: A new direction in modelingreal world problems with crossover effect, Math Biosci Eng. 2022;19:3526–63. https://doi.org/10.3934/mbe.2022163. Search in Google Scholar PubMed
[38] Pérez JES, Aguilar JFG, Atangana A. Novel numerical method for solving V-O fractional differential equations with power, exponential and Mittag-Leffler laws. Chaos Solit Fract. 2018;114:175–85. https://doi.org/10.1016/j.chaos.2018.06.032. Search in Google Scholar
[39] Alkahtani BST, Koca I, Atangana A. A novel approach of variable order derivative: Theory and methods. J Nonlin Sci Appl. 2016;9:4867–76. http://dx.doi.org/10.22436/jnsa.009.06.122. Search in Google Scholar
[40] Atangana A. On the stability and convergence of the time-fractional V-O telegraphequation, J Comput Phys. 2015;293:104–14. https://doi.org/10.1016/j.jcp.2014.12.043. Search in Google Scholar
[41] Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm Sci. 2016;20:763–9. https://doi.org/10.48550/arXiv.1602.03408. Search in Google Scholar
[42] Kumar S, Kumar A, Baleanu D. Two analytical methods for time-fractional nonlinear coupled Boussinesq-Burgeras equations arise in propagation of shallow water waves, Nonlin Dyn. 2016;1:1–17. https://doi.org/10.1007/s11071-016-2716-2. Search in Google Scholar
[43] Zhuang P, Liu F, Anh V, Turner I. Numerical methods for the V-O fractional advectiondiffusion equation with a nonlinear source term. SIAM J Numer Anal. 2009;47:1760–81. https://doi.org/10.1137/080730597. Search in Google Scholar
[44] Nisa KS, Farman M, Abdel-Aty M, Cao J. A review of the singular and non-singular kernels and their applications. Prog Fract Differ Appl. 2023;9:507–44. 10.18576/pfda/090401Search in Google Scholar
[45] Rashid S, Hamidi SZ, Akram S, Aon M, Elagan SK, Alsubei SMT. Theoretical and mathematical codynamics of nonlinear tuberculosis and COVID-19 model pertaining to fractional calculus and probabilistic approach. Sci Rep. 2024;14(1). 10.1038/s41598-024-59261-7Search in Google Scholar PubMed
[46] Rashid S, Jarad F. Novel investigation of stochastic fractional differential equations measles model via the white noise and global derivative operator depending on Mittag-Leffler kernel. Comp Model Engin Sci. 2024;139(3). 10.32604/cmes.2023.028773Search in Google Scholar
[47] Xu C, Farman M. Dynamical transmission and mathematical analysis for ebola virus in society by using constant proportional operator with power law kernel. Fractal Fractional. 2023;7:706. 10.3390/fractalfract7100706Search in Google Scholar
[48] Chu YM, Rashid S, Alzahrani T, Alhulayyil H, Alsagri H, Rehman S. Complex adaptive learning cortical neural network systems for solving time-fractional difference equations with bursting and mixed-mode oscillation behaviours. Sci Rep. 2024;13(1). 10.1038/s41598-023-48873-0Search in Google Scholar PubMed PubMed Central
[49] Du F, Lu JG. New criteria for finite-time stability of fractional order memristor-based neural networks with time delays. Neurocomputing. 2021;421:349–59. 10.1016/j.neucom.2020.09.039Search in Google Scholar
[50] Abdeljawad T, Mert R, Torres DF. Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations. In: Fractional derivatives with Mittag-Leffler Kernel. Cham, Switzerland: Springer; 2019. p. 35–47. Search in Google Scholar
[51] You X, Song Q, Zhao Z. Global Mittag-Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delay. Neural Netw. 2020;122:382–94. 10.1016/j.neunet.2019.11.004Search in Google Scholar PubMed
[52] Pratap A, Raja R, Cao J, Huang C, Niezabitowski M, Bagdasar O. Stability of discrete-time fractional-order time-delayed neural networks in complex field. Math Meth Appl Sci. 2021;44:419–40. 10.1002/mma.6745Search in Google Scholar
[53] Huang LL, Park JH, Wu GC, Mo ZW. Variable-order fractional discrete-time recurrent neural networks. J Comput Appl Math. 2020;370:112633. 10.1016/j.cam.2019.112633Search in Google Scholar
[54] Abdeljawad T, Baleanu D. Integration by parts and its applications of a new non-local derivative with Mittag-Leffler non-singular kernel. J Nonlin Sci Appl. 2017;10(3):1098–107. 10.22436/jnsa.010.03.20Search in Google Scholar
[55] Abdeljawad T. Fractional operators with generalized Mittag-Leffler kernels and their iterated differintegrals. Chaos. 2019;29(2):023102. 10.1063/1.5085726Search in Google Scholar PubMed
[56] Abdeljawad T, On delta and nabla Caputo fractional differences and dual identities. Discr Dyn Nat Soc. 2013;2013:1–12. 10.1155/2013/406910Search in Google Scholar
[57] Abdeljawad T. Different type kernel h-fractional differences and their fractional-sums. Chaos Solit Fract. 2018;116:146–56. 10.1016/j.chaos.2018.09.022Search in Google Scholar
[58] Abdeljawad T. Fractional difference operators with discrete generalized Mittag-Leffler kernels. Chaos Solit Fract. 2019;126:315–24. 10.1016/j.chaos.2019.06.012Search in Google Scholar
[59] Al-Qurashi M, Asif QU, Chu YM, Rashid S, Elagan SK. Complexity analysis and discrete fractional difference implementation of the Hindmarsh-Rose neuron system. Res Phys. 2023;51:106627. 10.1016/j.rinp.2023.106627Search in Google Scholar
[60] Al-Qurashi M, Rashid S, Jarad F, Ali E, Egami RH, Dynamic prediction modelling and equilibrium stability of a fractional discrete biophysical neuron model. Res Phy. 2023;48:106405. 10.1016/j.rinp.2023.106405Search in Google Scholar
[61] Baleanu D, Etemad S, Mohammadi H, Rezapour S. A novel modeling of boundary value problems on the glucose graph. Commun Nonlin Sci Numer Sim. 2021;100:105844. 10.1016/j.cnsns.2021.105844Search in Google Scholar
[62] Baleanu D, Jajarmi A, Mohammadi H, Rezapour S. A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative. Chaos Solit Fract. 2020;134:109705. 10.1016/j.chaos.2020.109705Search in Google Scholar
[63] Tuan NH, Mohammadi H, Rezapour S. A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos Solit Fract. 2020;140:110107. 10.1016/j.chaos.2020.110107Search in Google Scholar PubMed PubMed Central
[64] Aydogan SM, Hussain A, Sakar FM. On a nonlinear fractional order model of novel coronavirus (nCoV-2019) under AB-fractional derivative. J Math Extension. 2021;15. Search in Google Scholar
[65] Chu YM, Rashid S, Asif QUA, Abdalbagi M. On configuring new choatic behaviours for a variable fractional-order memristor-based circuit in terms of Mittag-Leffler kernel. Res Phy. 2023;53(1–4):106939. 10.1016/j.rinp.2023.106939Search in Google Scholar
[66] Peng Y, Liu J, He S, Sun K. Discrete fracmemristor-based chaotic map by Gürunwald-Letnikov difference and its circuit implementation. Chaos Solit Fract. 2023;171:113429. 10.1016/j.chaos.2023.113429Search in Google Scholar
[67] Ma M, Lu Y, Li Z, Sun Y, Wang C. Multistability and phase synchronization of Rulkov neurons coupled with a locally active discrete memristor. Fractal Fract. 2023;7:82. 10.3390/fractalfract7010082Search in Google Scholar
[68] Aydogan SM. On a k-dimensional system of hybrid fractional differential equations with multi-point boundary conditions. J Math Extension. 2021;15. Search in Google Scholar
[69] Chu YM, Rashid S, Karim S, Khalid A, Elagan SK. Deterministic-stochastic analysis of fractional differential equations malnutrition model with random perturbations and crossover effects. Sci Rep. 2023;13:14824. Search in Google Scholar
[70] Samei ME, Zanganeh H, Aydogan SM. To investigate a class of the singular fractional integro-differential quantum equations with multi-step methods. J Math Extension. 2021;15. Search in Google Scholar
[71] Chu YM, Rashid S, Karim S, Khalid A, Elagan SK, Deterministic-stochastic analysis of fractional differential equations malnutrition model with random perturbations and crossover effects. Sci Rep. 2023;13:15465. 10.1038/s41598-023-41861-4Search in Google Scholar PubMed PubMed Central
[72] Khan H, Alam K, Gulzar H, Etemad S, Rezapour S. A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations. Math Comput Sim. 2022;198:455–73. 10.1016/j.matcom.2022.03.009Search in Google Scholar
[73] Tusi APM, Jones AJ. The control of higher dimensional chaos: comparative results for the chaotic spacecraft attitude control problem. Phys D. 2000;135:41–62. 10.1016/S0167-2789(99)00114-1Search in Google Scholar
[74] Kuang J, Tan SH, Leung AYT. Chaotic attitude motion of spacecrafts under small perturbation torques, J Sound Vib. 2000;235:175–200. 10.1006/jsvi.1999.2926Search in Google Scholar
[75] Kuang J, Tan S, Arichandran K, Leung AYT. Chaotic dynamics of an asymmetrical gyrostat. Int J Non Linear Mech 2001;36:1213–33. 10.1016/S0020-7462(00)00091-3Search in Google Scholar
[76] Kong LY, Zhoul FQ, Zou I. The control of chaotic attitude motion of a perturbed spacecraft. In: Proceedings of the 25th Chinese control conference-2006 Harbin, Heilongjiang, 7-11 Aug, 2006. 10.1109/CHICC.2006.280796Search in Google Scholar
[77] Kumar S, Matouk AE, Chaudhary H, Kant S. Control and synchronization of fractional-order chaotic spacecraft systems using feedback and adaptive control techniques. Int J Adapt Control Signal Process. 2020;1–14. 10.1002/acs.3207Search in Google Scholar
[78] VanDyke MC, Hall CD. Decentralized coordinated attitude control within aformation of spacecraft. J Guid Cont Dyn. 2006;29(5):1101–9. 10.2514/1.17857Search in Google Scholar
[79] Liang K, Wang J, Sun Z. Robust decentralized coordinated attitude control ofspacecraft formation, Acta Astronaut. 2011:69(5–6):280–8. 10.1016/j.actaastro.2011.03.018Search in Google Scholar
[80] Abdeljawad T, Mert R, Torres DFM, Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations. In Fractional Derivatives with Mittag-Leffler Kernel. Cham, Switzerland: Springer; 2019. p. 35–47. 10.1007/978-3-030-11662-0_3Search in Google Scholar
[81] Čermák J, Gyõri I, Nechvátal L, On explicit stability conditions for a linear fractional difference system. Fract Calc Appl Anal. 2015;18:651–72. 10.1515/fca-2015-0040Search in Google Scholar
[82] Sadaoui D, Boukabou A, Merabtine N, Benslama M. Predictive synchronization ofchaotic spacecrafts systems. Expert Sys Appl. 2011;38(7):9041–5. 10.1016/j.eswa.2011.01.117Search in Google Scholar
[83] Matignon D, Stability properties for generalized fractional differential systems. In ESAIM: Proceedings. EDP Sciences; 1998. vol. 5. p. 145–58. 10.1051/proc:1998004Search in Google Scholar
[84] Franco-Pérez L, Fernández-Anaya G, Quezada-Téllez LA. On stability of nonlinear nonautonomous discrete fractional Caputo systems. J Math Anal Appl. 2020;487:124021. 10.1016/j.jmaa.2020.124021Search in Google Scholar
[85] Hu QL, Shi YX, Shao XD. Adaptive fault-tolerant attitude control for satellite reorientation under input saturation. Aerosp Sci Tech. 2018;78:171–82. 10.1016/j.ast.2018.04.015Search in Google Scholar
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- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
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Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
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- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
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- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
- Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
