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Abstrakty
Synchronization of fractional order systems has gained great interest in various research activities in recent years. The aim of this study is to investigate the synchronization of a class of neural network systems with respect to the proportional Caputo fractional order derivative. Using the generalized Gronwall inequality, a sufficient condition that possesses the exponential convergence rate, presents and demonstrates that the error of the proposed system converges to zero. Two illustrative numerical examples are provided to show the applicability and validity of the obtained theoretical results.
Rocznik
Tom
Strony
76--88
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
autor
- Department of Mathematics, College of Science, Kuwait University, Safat, Kuwait
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
autor
- Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia
autor
- Department of Mathematics, College of Science, Kuwait University, Safat, Kuwait
autor
- Department of Mathematics, College of Science, Kuwait University, Safat, Kuwait
Bibliografia
- 1. Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier.
- 2. Koeller, R. (1984). Applications of fractional calculus to the theory of viscoelasticity. ASME Journal of Applied Mechanics, 51, 299-307.
- 3. Lazarevi´c, M.P. (2006). Finite time stability analysis of PDα fractional control of robotic time-delay systems. Mechanics Research Communications, 33(2), 269-279.
- 4. Nagy, A.M. (2022). Numerical solutions for nonlinear multi-term fractional differential equations via Dickson operational matrix. International Journal of Computer Mathematics, 99(7), 1505-1515.
- 5. Nagy, A.M., Assidi, S., & Makhlouf, A.B. (2022). Convergence of solutions for perturbed and unperturbed cobweb models with generalized Caputo derivative. Boundary Value Problem, 2022, 89.
- 6. Lynch, V.E., Carreras, B.A., del-Castillo-Negrete, D., Ferreira-Mejias, K.M., & Hicks, H.R. (2003). Numerical methods for the solution of partial differential equations of fractional order. Journal of Computational Physics, 192(2), 406-421.
- 7. Baleanu D., Jajarmi, A., Mohammadi, H., & Rezapour, S. (2020). A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative. Chaos, Solitons & Fractals, 134, 109705.
- 8. Mohammadi, H., Kumar, S., Rezapour, S., & Etemad, S. (2021). A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control. Chaos, Solitons & Fractals, 144, 110668.
- 9. Khan, H., Alam, K., Gulzar, H., Etemad, S., & Rezapour, S. (2022). A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations. Mathematics and Computers in Simulation, 198, 455-473.
- 10. Yadav, P., Jahan, S., & Nisar, K.S. (2023). Fractional order mathematical model of Ebola virus under Atangana-Baleanu-Caputo operator. Results in Control and Optimization, 13, 100332.
- 11. Wali, M., Arshad, S., Eldin, S.M., & Siddique, I. (2023). Numerical approximation of Atangana-Baleanu Caputo derivative for space-time fractional diffusion equations. AIMS Mathematics, 8(7), 15129-15147.
- 12. Bohner, M., Hristova, S., Malinowska, A.B., Morgado, M.L., & Almeida, R. (2022). A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol. Communications in Nonlinear Science and Numerical Simulation, 115, 106756.
- 13. Boucenna, D., Baleanu, D., Ben Makhlouf, A., & Nagy, A.M. (2021). Analysis and numerical solution of the generalized proportional fractional Cauchy problem. Applied Numerical Mathematics, 167, 173-186.
- 14. Ahmad, M., Zada, A., Ghaderi, M., George, R., & Rezapour, S. (2022). On the existence and stability of a neutral stochastic fractional differential system. Fractal Fractional, 6, 203.
- 15. Akg¨ul, A., & Baleanu, D. (2021). Analysis and applications of the proportional Caputo derivative. Advances in Difference Equations, 2021, 136.
- 16. Jarad, F., Abdeljawad, T., & Alzabut, J. (2017). Generalized fractional derivatives generated by a class of local proportional derivatives. The European Physical Journal Special Topics, 226, 3457-3471.
- 17. Naifar, O., Nagy, A.M., Ben Makhlouf, A., Kharrat, M., & Hammami, M.A. (2019). Finitetime stability of linear fractional-order time-delay systems. International Journal of Robust and Nonlinear Control, 29(1), 180-187.
- 18. Rezapour, S., Deressa, C.T., & Etemad, S. (2021). On a memristor-based hyperchaotic circuitin the context of nonlocal and nonsingular kernel fractional operator. Journal of Mathematics, 2021, 6027246, 1-21.
- 19. Batiha, I.M., Albadarneh, R.B., Momani, S., & Jebril, I.H. (2020). Dynamics analysis of fractional-order Hopfield neural networks. International Journal of Biomathematics, 13(8), 2050083.
- 20. Huang, C.,Wang, H., & Cao, J. (2023). Fractional order-induced bifurcations in a delayed neural network with three neurons. Chaos, 33, 033143.
- 21. Liu, D., Zhu, S., & Chang, W. (2017). Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay. International Journal of Systems Science, 48(9), 1966-1977.
- 22. Li, T., Song, A.G., Fei, S.M., & Guo, Y.Q. (2009). Synchronization control of chaotic neural networks with time-varying and distributed delays. Nonlinear Analysis Theory, Methods Applications, 71, 2372-2384.
- 23. Zhang, X., & Yang, C. (2020). Neural network synchronization of fractional-order chaotic systems subject to backlash nonlinearity. AIP Advances, 10(6), 065110.
- 24. Wang, R., Zhang, Y., Chen, Y., Chen, X., & Xi, L. (2020). Fuzzy neural network-based chaos synchronization for a class of fractional-order chaotic systems: an adaptive sliding mode control approach. Nonlinear Dynamics, 100, 1275-1287.
- 25. Erdelyi, A. (1953). Higher Transcendental Functions. Vol. III, New-York: McGraw-Hill.
- 26. Ye, H., Gao, J., & Ding, Y. (2007). A generalized Gronwall inequality and its application to a fractional differential equation. Journal of Mathematical Analysis and Applications, 328(2), 1075-1081.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-674128c9-5590-4053-ac1c-9bd31c2c6c26
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