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

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Original research article

Author(s):

Adel Lachouri^a, Abdelouaheb Ardjouni^b

^a Department of Mathematics, Annaba University, Annaba, Algeria.
^b Department of Mathematics and Informatics, Souk Ahras University, Souk Ahras, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 6 (1), 101-117.

Received: April 15, 2021

Accepted: December 22, 2021

Published: December 28, 2021

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.

Keywords: ξ-Hilfer fractional integro-differential equation; Existence; Uniqueness; Ulam–Hyers stability; Fixed point theorems.

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APA Style

Lachouri, A., & Ardjouni, A. (2022). The existence and Ulam-Hyers stability results for generalized Hilfer fractional integro-differential equations with nonlocal integral boundary conditions. Advances in the Theory of Nonlinear Analysis and its Application , 6 (1), 101-117.