On the Ulam-Hyers-Rassias stability for a boundary value problem of implicit ?-Caputo fractional integro-differential equation

Abstract

The main purpose of this paper is to study the existence and uniqueness of a nonlinear implicit ?-Caputo fractional order integro-differential boundary value problem using Schauder’s and Banach’s fixed point theorems. Besides, we study its stability using Ulam-Hyers-Rassias stability type. Finally, we demonstrate our main findings, with a particular case example included to show the significance of our results.