Existence and stability analysis for nonlinear ψ-Hilfer fractional differential equations with nonlocal integral boundary conditions

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Sciences, University of Annaba, Annaba, Algeria

2 Department of Mathematics and Informatics, University of Souk Ahras, Souk Ahras, Algeria

3 Laboratory of Analysis and Control of Differential Equations,University of 8 May 1945 Guelma, Algeria

Abstract

In this paper, we study the existence and uniqueness of mild solutions for nonlinear fractional differential equations subject to nonlocal integral boundary conditions in the frame of a ψ-Hilfer fractional derivative. Further, we discuss different kinds of stability of Ulam-Hyers for mild solutions to the given problem. Using the fixed point theorems together with generalized Gronwall inequality the desired outcomes are proven. The obtained results generalize many previous works that contain special cases of function ψ. At the end, some pertinent examples demonstrating the effectiveness of the theoretical results are presented.

Keywords