A new class of mixed fractional differential equations with integral boundary conditions

Djiab Somia; Nouiri Brahim

doi:10.2478/mjpaa-2021-0016

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A new class of mixed fractional differential equations with integral boundary conditions

Moroccan Journal of Pure and Applied Analysis

Volume 7 (2021): Issue 2 (May 2021)

By: Djiab Somia and Nouiri Brahim

Open Access

|Dec 2020

Abstract

This paper deals with a new class of mixed fractional differential equations with integral boundary conditions. We show an important equivalence result between our problem and nonlinear integral Fredholm equation of the second kind. The existence and uniqueness of a positive solution are proved using Guo-Krasnoselskii’s fixed point theorem and Banach’s contraction mapping principle. Different types of Ulam-Hyers stability are discussed. Three examples are also given to show the applicability of our results.

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