Abstract
In this paper, the stability of conformable fractional-order nonlinear systems depending on a parameter is presented and described. Furthermore, The design of a feedback controller for the same class of conformable fractional-order systems is introduced. Illustrative examples are given at the end of the paper to show the effectiveness of the proposed results.
References
[1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66. 10.1016/j.cam.2014.10.016Search in Google Scholar
[2] B. Ben Hamed, Z. Haj Salem and M. A. Hammami, Stability of nonlinear time-varying perturbed differential equations, Nonlinear Dynam. 73 (2013), no. 3, 1353–1365. 10.1007/s11071-013-0868-xSearch in Google Scholar
[3] A. Ben Makhlouf, M. A. Hammami and K. Sioud, Stability of fractional-order nonlinear systems depending on a parameter, Bull. Korean Math. Soc. 54 (2017), no. 4, 1309–1321. Search in Google Scholar
[4] N. Engheta, On fractional calculus and fractional multipoles in electromagnetism, IEEE Trans. Antennas and Propagation 44 (1996), no. 4, 554–566. 10.1109/8.489308Search in Google Scholar
[5] M. Eslami, Solitary wave solutions for perturbed nonlinear Schrodingers equation with Kerr law nonlinearity under the DAM, Optik 126 (2015), 1312–1317. 10.1016/j.ijleo.2015.02.075Search in Google Scholar
[6] B. Ghanmi, Stability of impulsive systems depending on a parameter, Math. Methods Appl. Sci. 39 (2016), no. 10, 2626–2646. 10.1002/mma.3717Search in Google Scholar
[7] H. A. Ghany, A. Hyder and M. Zakarya, Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives, Chinese Phys. B 29 (2020), 1–15. 10.1088/1674-1056/ab75c9Search in Google Scholar
[8] S. He, K. Sun, K. Mei, B. Yan and S. Xu, Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative, European Phys. J. Plus 36 (2017), 1–10. 10.1140/epjp/i2017-11306-3Search in Google Scholar
[9] Y. Hong, Finite-time stabilization and stabilizability of a class of controllable systems, Systems Control Lett. 46 (2002), no. 4, 231–236. 10.1016/S0167-6911(02)00119-6Search in Google Scholar
[10] O. S. Iyiola, O. Tasbozan, A. Kurt and Y. Çenesiz, On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion, Chaos Solitons Fractals 94 (2017), 1–7. 10.1016/j.chaos.2016.11.003Search in Google Scholar
[11] A. Jmal, M. Elloumi, O. Naifar, A. Ben Makhlouf and M. A. Hammami, State estimation for nonlinear conformable fractional-order systems: A healthy operating case and a faulty operating case, Asian J. Control 22 (2020), 1870–1879. 10.1002/asjc.2122Search in Google Scholar
[12] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70. 10.1016/j.cam.2014.01.002Search in Google Scholar
[13]
A. Korkmaz,
Exact solutions to
[14] A. Korkmaz and K. Hosseini, Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods, Opt. Quantum Electron. 49 (2017), 1–10. 10.1007/s11082-017-1116-2Search in Google Scholar
[15] N. Laskin, Fractional market dynamics, Phys. A 287 (2000), no. 3–4, 482–492. 10.1016/S0378-4371(00)00387-3Search in Google Scholar
[16] A. Oustaloup, La Dérivation Non Entière, théorie, synthèse et applications, Hermes, Paris, 1995. Search in Google Scholar
[17] Q. Shen, D. Wang, S. Zhu and E. K. Poh, Finite-time fault-tolerant attitude stabilization for spacecraft with actuator saturation, IEEE Trans. Aerospace Electron. Syst. 451 (2015), 2390–2405. 10.1109/TAES.2015.130725Search in Google Scholar
[18] A. Souahi, O. Naifar, A. Ben Makhlouf and M. A. Hammami, Discussion on Barbalat lemma extensions for conformable fractional integrals, Internat. J. Control 92 (2019), no. 2, 234–241. 10.1080/00207179.2017.1350754Search in Google Scholar
[19] H. Sun, A. Abdelwahad and B. Onaral, Linear approximation of transfer function with a pole of fractional order, IEEE Trans. Automat. Contr. 29 (1984), 441–444. 10.1109/TAC.1984.1103551Search in Google Scholar
[20] O. Tasbozan, Y. Cenesiz and A. Kurt, New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method, European Phys. J. Plus 131 (2016), 1–10. 10.1140/epjp/i2016-16244-xSearch in Google Scholar
[21] I. Torres, J. C. Fabris and O. F. Piattella, Quantum cosmology of fab four John theory with conformable fractional derivative, Universe 6 (2020), 10.3390/universe6040050. 10.3390/universe6040050Search in Google Scholar
[22] B. Xin, W. Peng and L. Guerrini, A continuous time Bertrand duopoly game with fractional delay and conformable derivative: Modeling, discretization process, Hopf bifurcation, and chaos, Front. Phys. 7 (2019), 84–93. 10.3389/fphy.2019.00084Search in Google Scholar
[23] A. Zavala-Río, I. Fantoni and G. Sanahuja, Finite-time observer-based output-feedback control for the global stabilisation of the PVTOL aircraft with bounded inputs, Internat. J. Systems Sci. 47 (2016), no. 7, 1543–1562. 10.1080/00207721.2014.938906Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations
Articles in the same Issue
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations