Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana–Baleanu–Caputo Derivative under Integral Boundary Conditions

Abstract

In this study, we consider the existence results of solutions of impulsive Atangana–Baleanu–Caputo $\left(\mathcal{A}\mathcal{B}\mathcal{C}\right)$ fractional integro-differential equations with integral boundary conditions. Krasnoselskii’s fixed-point theorem and the Banach contraction principle are used to prove the existence and uniqueness of results. Moreover, we also establish Hyers–Ulam stability for this problem. An example is also presented at the end.