Abstract
In this paper, we study the stability of nonlinear fractional neutral systems equipped with the Caputo derivative. We extend the Lyapunov-Krasovskii approach for the nonlinear fractional neutral systems. Conditions of uniform stability are obtained for the nonlinear fractional neutral systems.
Highlights
In recent decades, fractional calculus and fractional differential equations have attracted great attention
For more details about the stability results and the methods available to analyze the stability of fractional differential equations, the reader may refer to the recent survey papers [, ] and the references therein
4 Conclusions In this paper, we have studied the stability of nonlinear fractional order neutral systems
Summary
Fractional calculus and fractional differential equations have attracted great attention. For more details about the stability results and the methods available to analyze the stability of fractional differential equations, the reader may refer to the recent survey papers [ , ] and the references therein. In [ , ], the fractional Lyapunov’s second method was proposed, and the authors extended the exponential stability of integer order differential system to the Mittag-Leffler stability of fractional differential system. We consider the stability of a class of nonlinear fractional neutral functional differential equations with the Caputo derivative. Motivated by Li et al [ , ], Baleanu et al [ ] and Cruz and Hale [ ], we aim in this paper to extend the Lyapunov-Krasovskii method for the nonlinear fractional neutral systems.
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