Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations

Abstract

In this article, we prove some new uniqueness and Ulam-Hyers stability results of a nonlinear generalized fractional integro-differential equation in the frame of Caputo derivative involving a new kernel in terms of another function ψ. Our approach is based on Babenko’s technique, Banach’s fixed point theorem, and Banach’s space of absolutely continuous functions. The obtained results are demonstrated by constructing numerical examples.