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

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 stabil...

Full description

Saved in:
Bibliographic Details
Published inAdvances in the theory of nonlinear analysis and its applications Vol. 6; no. 1; pp. 101 - 117
Main Authors LACHOURİ, Adel, ARDJOUNİ, Abdelouaheb
Format Journal Article
LanguageEnglish
Published 31.03.2022
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2587-2648
2587-2648
DOI:10.31197/atnaa.917180