The existence and Ulam-Hyers stability results for generalized Hilfer fractional integro-differential equations with nonlocal integral boundary conditions

Abstract

In this paper, we study the existence and uniqueness of mild solutions for nonlinear fractional integro-differential equations (FIDEs) subject to nonlocal integral boundary conditions (nonlocal IBC) in the frame of a ξ-Hilfer fractional derivative (FDs). Further, we discuss different kinds of stability of Ulam-Hyers (UH) for mild solutions to the given problem. Using the fixed point theorems (FPT's) together with generalized Gronwall inequality the desired outcomes are proven. Examples are given which illustrate the effectiveness of the theoretical results.