Band 24, Heft 6

Many biophysical effects of electromagnetic radiation are interpreted based on the induced voltage on cellular membranes. It is very instructive to study wideband frequency responses showing how an impinging electromagnetic wave carrying a certain time waveform translates into a time-dependent change in the cell-membrane potentials in any desired tissue. A direct numerical solution of this problem with realistic models for the body and cells results in meshcells of nanometer dimensions, which is unaffordable for almost any computing machine. In this paper, we exploit a multiscale method with serial frequency responses to arrive at the final frequency response for the induced transmembrane potential changes in cerebral cells induced by electromagnetic waves incident on the body. The results show a bandpass characteristic; a frequency window of approximately 10 kHz to 100 MHz as the most sensitive frequency band for neuronal membrane sensing of external electromagnetic fields.

This manuscript investigates the issue of existence results for fractional differential evolution inclusions of order r ∈ (1, 2) in the Banach space. In the beginning, we analyze the existence results by referring to the fractional calculations, cosine families, multivalued function, and Martelli’s fixed point theorem. The result is also used to investigate the existence of nonlocal fractional evolution inclusions of order r ∈ (1, 2). Finally, a concrete application is given to illustrate our main results.

The optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential and mixed fractional Brownian motion is investigated in this article. The deterministic nonlinear second-order controlled partial differential system is enriched with stochastic perturbations, non-instantaneous impulses, and Clarke subdifferential. In particular, the nonlinearities in the system that rely on the state of the solution are allowed to rely on the corresponding probability distribution of the state. The solvability of the considered system is discussed with the help of stochastic analysis, multivalued analysis, and multivalued fixed point theorem. Further, the existence of optimal control is established with the aid of Balder’s theorem. Finally, an example is provided to illustrate the developed theory.

In this article, we propose generalized forms of three well-known fractional numerical methods namely Euler, Runge–Kutta 2-step, and Runge–Kutta 4-step, respectively. The new versions we provide of these methods are derived by utilizing a non-uniform grid which is slightly different from previous versions of these algorithms. A new generalized form of the well-known Caputo-type fractional derivative is used to derive the results. All necessary analyses related to the stability, convergence, and error bounds are also provided. The precision of all simulated results is justified by performing multiple numerical experiments, with some meaningful problems solved by implementing the code in Mathematica . Finally, we give a brief discussion on the simulated results which shows that the generalized methods are novel, effective, reliable, and very easy to implement.

In this article, we examine a coupled system of fractional integrodifferential equations of Liouville–Caputo form with instantaneous impulsive conditions in a Banach space. We obtain the existence and uniqueness results by applying the theory of fixed point theorems. In a similar manner, we discuss Hyers–Ulam stability and controllability. We also present an example to show the validity of the obtained results.

In this paper, we construct a new generalized result to study the existence of solutions of nonlinear fractional boundary value problems (FBVPs). The proposed results unify the existence criteria of certain FBVPs including periodic and antiperiodic as special cases that have been previously studied separately in the literature. The method we employ is topological in its nature and manifests themselves in the forms of differential inequalities (lower and upper solutions, and coupled lower and upper solutions (CLUSs)). Two examples are given to demonstrate the applicability of the developed theoretical results.

In this article, our work oversees with the nonlocal coupled complex modified Korteweg–de Vries equations (cmKdV), which is a nonlocal generalization for coupled cmKdV equations. The n -fold Darboux transformation (DT) is constructed in the form of determinants for the nonlocal coupled cmKdV equations. Via generalized DT method, we obtain the rational soliton solutions describing M -shaped soliton, W -shaped soliton, and the interactions on the plane wave and periodic background. The results can be useful to study the dynamical behaviors of soliton solutions in nonlocal wave models.

This study numerically investigates the two-dimensional natural convection in a square enclosure with an isothermal diamond elliptic array at Rayleigh numbers of 10 4 ≤ Ra ≤ 10 7 . Three cases are considered, i.e., case 1 where two pairs of circular heating bodies are used inside the cavity, one is placed on the vertical centerline (VC) of the cavity and the other on the horizontal centerline (HC), case 2 where one pair of horizontal elliptic heating bodies is placed on the VC of the cavity and the other on the HC and case 3 where the horizontal elliptic heating bodies are replaced by vertical elliptic heating bodies. Numerical simulation was carried out based on the mesoscopic approach (LBM). The effects of the horizontally and vertically heated arrays were investigated. We demonstrate that, only when the Rayleigh number increases to Ra = 10 7 , the numerical solutions reach an unsteady state for all cases. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder.

The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von–Neumann method. Taylor’s expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of τ on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.

Fractional theories have gained recently an increasing interest in dynamical systems since they offer some solutions to a number of puzzles in particular nonconservative and dissipative issues. Most of fractional dynamical theories are formulated by means of one occurrence of action that group kinetic energy and potential energy in one single package. In this work, we introduce a modified fractional dynamics based on the occurrence of two independent actions where fractional and nonfractional Euler–Lagrange equations are mixed together. We show that their combination divulge some properties that offer new insights in nonlinear dynamics. In particular, it was observed that a large family of solutions that could be used to model dissipative systems may be derived from the action with two occurrences of integrals. Moreover, damping systems may be obtained by means of simple Lagrangian functionals.

In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N -soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

In this paper, the fixed-time synchronization analysis is addressed for a class of discontinuous neutral-type neural networks. The focus is mainly on the design of useful control laws such that the constructed error system converges to zero in a fixed time. The major difficulty is to cope with the discontinuous neuron activations, D operators, time-varying discrete, and distributed delays simultaneously. To accomplish the target, a new and effective framework is firstly established. By means of functional differential inclusions theory, inequality technique and Lyapunov–Krasovskii functional, novel discontinuous feedback controllers are designed and some new verifiable algebraic criteria are derived to design the control gains. In contrast to the existed results on the neutral-type neural networks, the theoretical results of this paper are more general and rigorous. Finally, numerical examples and simulations are presented to illustrate the correctness of the main results.

In this paper, we study a type of nonlinear hybrid Δ-difference equations of fractional-order. The main objective is to establish some stability criteria including the Ulam–Hyers stability, generalized Ulam–Hyers stability together with the Mittag-Leffler–Ulam–Hyers stability for the addressed problem. Prior to the stabilization processes, solvability criteria for the existence and uniqueness of solutions are considered. For this purpose, a hybrid fixed point theorem for triple operators and the Banach contraction mapping principle are applied, respectively. For the sake of illustrating the practical impact of the proposed theoretical criteria, we finish the paper with particular examples.

In this paper, the boundedness of the Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of the p -adic fractional Hausdorff operator on weighted p -adic weak Lebesgue spaces. We also obtain the sufficient condition of commutators of the p -adic fractional Hausdorff operator by taking symbol function from Lipschitz spaces. Moreover, strong type estimates for fractional Hausdorff operator and its commutator on weighted p -adic Lorentz spaces are also acquired.

In the present investigation, a two-dimensional (2D) finite element (FE) model of closed-cell AlSi12Mg1Cu1 alloy foam (AAFs) of 0.35 relative density of different cell shapes, i.e., square, hexagonal, octagonal, and circular shaped cell established with the help of ABAQUS simulation software. Experimentation is also done for 0.35 relative density metal foam to report its compressive behavior. The plateau stress σ p l $\left(\right.{\sigma }_{pl}$ ) and energy absorption capacity ( E ab ) of AAFs ( ρ rd = 0.35) properties are calculated from the plotted stress–strain graph and a significant effect of cell shape on compressive performance observed. By SEM characterization, it was noted that the experimental specimen also had near circular cells. The strength and energy absorption values are calculated for square-shape, circular-shaped, octagonal-shaped, and hexagonal-shaped cells in descending order from maximum to minimum. A convergence study is also carried out concerning the number of elements to obtain the most accurate FE results.

Many researchers have tried to predict the impact of the COVID-19 outbreak on morbidity, in order to help policy-makers find optimal isolation policies. However, despite the development and use of many models and sophisticated tools, these forecasting attempts have largely failed. We present a model that considers the severity of the disease and the heterogeneity of contacts between the population in complex space–time dynamics. Using mathematical and computational methods, the applied tool was developed to analyze and manage the COVID-19 pandemic (from an epidemiological point of view), with a particular focus on population heterogeneity in terms of age, susceptibility, and symptom severity. We show improved strategies to prevent an epidemic outbreak. We evaluated the model in three countries, obtaining an average mean square error of 0.067 over a full month of the basic reproduction number ( R 0 ). The goal of this study is to create a theoretical framework for crisis management that integrates accumulated epidemiological considerations. An applied result is an open-source program for predicting the outcome of an isolation strategy for future researchers and developers who can use and extend our model.

The 3D quenching problem reflecting solid-burn scene based on convection–reaction–diffusion equation is creatively concerned in this work. The spatial derivatives of original equation are discretized by Taylor series and the temporal derivatives are approximated by the Crank–Nicolson (CN) method. After the discrete schemes are arranged, an alternating direction implicit (ADI) scheme on adaptive grid is constructed to interpret quenching phenomena of the three-dimension (3D) equation with singularity source. Quenching time, quenching domain, and characteristics relative to temperature as well as variation of temperature over time are achieved via scientific experiment and analysis. Comparing with the 1D or 2D problem, it is harder for the 3D problem to produce quenching phenomena. Regardless of different convection functions, it can form quenching behaviors through experiments when only the elements which include degeneracy parameter, convection parameters, and domain sizes are configured properly. We hope all this can offer references for the 3D engineering problem. At the same time, it will offer support to research the relationship between quenching phenomena and degeneracy parameter, convection parameters, and domain sizes in the future, respectively.

In this paper, we investigate the sufficient conditions for null controllability of noninstantaneous impulsive Hilfer fractional stochastic integrodifferential system with the Rosenblatt process and Poisson jump. The required results are obtained based on fractional calculus, stochastic analysis, and Sadovskii’s fixed point theorem. Finally, an example is given to illustrate the obtained results.

The paper deals with the application of a strong method called the modified Mickens iteration technique which is used for solving a strongly nonlinear system. The system describes the motion of a simple mathematical pendulum with a particle attached to it through a stretched wire. This model has great applications especially in the area of nonlinear vibrations and oscillation systems. The proposed method depends on determining the frequency and amplitude of the system through the modified Mickens iterative approach which is a modification of the regular Mickens approach. The preliminaries of the proposed technique are present and the application to the model is discussed. The method depends on the Mickens iteration approach which transforms the considered equation into a linear form and then is solving this equation result in the approximate solution. Some examples are given to validate and illustrate the effectiveness and convenience of the method. These results are compared with other relative techniques from the literature in terms of finding the frequency of the two examined models. The method produces more accurate results when compared to these methods and is considered a strong candidate for solving other nonlinear problems with applications in science and engineering.

Calcium signaling in nerve cells is a crucial activity for the human brain to execute a diversity of its functions. An alteration in the signaling process leads to cell death. To date, several attempts registered to study the calcium distribution in nerve cells like neurons, astrocytes, etc. in the form of the integer-order model. In this paper, a fractional-order mathematical model to study the spatiotemporal profile of calcium in nerve cells is assembled and analyzed. The proposed model is solved by the finite element method for space derivative and finite difference method for time derivative. The classical case of the calcium dynamics model is recovered by setting the fractional parameter and that validates the model for classical sense. The numerical computations have systematically presented the impact of a fractional parameter on nerve cells. It is observed that calbindin-D 28k provides a significant effect on the spatiotemporal variation of calcium profile due to the amalgamation of the memory of nerve cells. The presence of excess amounts of calbindin-D 28k controls the intracellular calcium level and prevents the nerve cell from toxicity.

In this manuscript, switched coupled system of nonlinear impulsive Langevin equations involving four Hilfer fractional-order derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss the existence, uniqueness, and Ulam’s type stability results of our proposed model, with the help of Schaefer’s fixed point theorem. An example is provided at the end to illustrate our results.

In this paper, a nonlinear energy sink is used to improve the dynamic behavior of a square plate in supersonic flow. The plate is examined with different boundary conditions. The effect of changing the parameters and installation location of nonlinear energy sink on improving the dynamic behavior of the plate has been studied. The governing equations are first obtained using Von Kármán’s plate theory and piston theory, and then discretized using the Rayleigh–Ritz process. These equations are then solved using the fourth-order Runge–Kutta method. Time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were used to investigate the dynamic behavior and impact of nonlinear energy sink. The results show that the dynamic behavior of the plate is very complex in some cases, but with proper use of nonlinear energy sinks, this behavior can be improved.