### Generalized Mittag-Leffler stability of nonlinear fractional regularized Prabhakar differential systems

Document Type : Research Paper

Authors

1 Department of Applied Mathematics and Computer Sciences, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran

2 Department of Applied Mathematics and Computer Sciences, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

Abstract

This work is devoted to study of  the stability analysis of generalized fractional nonlinear system including the regularized Prabhakar derivative. We present several criteria for the generalized Mittag-Leffler stability and the asymptotic stability of this system by using the Lyapunov direct method. Further, we provide two test cases to illustrate the effectiveness  of  results. We apply the numerical method to solve the generalized fractional system with the regularized Prabhakar fractional systems and reveal asymptotic stability behavior of the presented systems by employing numerical simulation.

Keywords

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###### Volume 12, Issue 2November 2021Pages 665-678
• Receive Date: 11 December 2019
• Revise Date: 22 December 2019
• Accept Date: 08 January 2020