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

Authors : Adel LACHOURİ, Abdelouaheb ARDJOUNİ

Pages : 101-117

Doi:10.31197/atnaa.917180

View : 14 | Download : 8

Publication Date : 2022-03-31

Article Type : Research Paper

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