Solution Estimates To Caputo Proportional Fractional Derivative Delay Integro-Differential Equations

Abstract

In this article, a class of scalar generalized Caputo proportional fractional derivative delay integro-differential equations (CPFrDIDEs) with multiple non-linear kernels and multiple time delays is considered. Fundamental qualitative behaviors of the solutions such as stability, asymptotic stability, exponential stability, and boundedness of solutions are investigated. The technique used in the proofs depend upon the modified Lyapunov-Razumikhin method (LRM). As numerical applications of the novel results of this article, four examples are constructed to demonstrate that the results are valid and applicable. The outcomes of this article allow novel contributions to qualitative theory of FrDIDEs.