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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Synchronization Methods for Chaotic Systems Involving Fractional Derivative with a Non-Singular Kernel

Journal of Applied Nonlinear Dynamics 11(2) (2022) 375--386 | DOI:10.5890/JAND.2022.06.008

Fatiha Mesdoui$^1$, Nabil Shawagfeh$^2$, Adel Ouannas$^3$

$^1$ University of Mohamed Seddik Benyahia, Jijel, Algeria

$^2$ Department of Mathematics, University of Jordan, Amman, Jordan

$^3$ Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi, Algeria

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Abstract

This study considers the problem of control-synchronization for chaotic systems involving fractional derivatives with a non-singular kernel. Using an extension of the Lyapunov Theorem for systems with Atangana-Baleanu-Caputo (ABC) derivative, a suitable control scheme is designed to achieve matrix projective synchronization (MP) between nonidentical ABC systems with different dimensions. The results are exemplified by the ABC version of the Lorenz system, Bloch system, and Liu system. To show the effectiveness of the proposed results, numerical simulations are performed based on the Adams-Bashforth-Mounlton numerical algorithm.

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