New Existence of Solutions for Fractional Integro-Differential Equations with Nonseparated Boundary Conditions

Lahcen Ibnelazyz,Khalid Hilal,Karim Guida,Said Melliani,Xinan Hao

doi:10.1155/2021/9915375

Abstract

Results reported in this article prove the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations supplemented by nonseparated boundary value conditions. We consider a new norm to establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle. Some examples are provided to illustrate the results.

Highlights

Fractional differential equations have been an important tool to describe many problems and processes in different fields of science
Fractional integro-differential equations were investigated by many researchers in different problems, and a lot of papers were published in this matter
Many boundary conditions were considered for the fractional-order integro-differential equations; some of these conditions are the classical, periodic, antiperiodic, nonlocal, multipoint, and the integral boundary conditions

Summary

Introduction

Fractional differential equations have been an important tool to describe many problems and processes in different fields of science. Fractional integro-differential equations were investigated by many researchers in different problems, and a lot of papers were published in this matter (see, for example, [14,15,16]). Motivated by the above discussion, in this paper, we establish the existence and uniqueness of solutions for a class of fractional integro-differential equations with nonseparated boundary value conditions as follows:. Our motivation comes from the fact that not many papers have considered the existence and uniqueness results of nonlinear integro-differential equations with nonseparated boundary conditions.

Preliminaries and Notations

Main Results

Conclusion