Razumikhin Qualitative Analyses of Volterra Integro-Fractional Delay Differential Equation With Caputo Derivatives

Abstract

A non-linear system of Volterra integro-fractional delay differential equations with Caputo fractional derivatives is considered. New sufficient conditions for uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solution of the unperturbed system, and the boundedness of all solutions of the perturbed system, are presented. The technique of proof involves the Razumikhin method with an appropriate Lyapunov function. For illustrative purposes, two examples are provided. (C) 2021 Published by Elsevier B.V.