Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions

Karim Guida,Lahcen Ibnelazyz,Khalid Hilal,Marianna Ruggieri

doi:10.1155/2020/8898292

Karim Guida, Lahcen Ibnelazyz + Show 2 more

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https://doi.org/10.1155/2020/8898292

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Abstract

This paper deals with the existence and uniqueness of solutions for a new class of coupled systems of Hilfer fractional pantograph differential equations with nonlocal integral boundary conditions. First of all, we are going to give some definitions that are necessary for the understanding of the manuscript; second of all, we are going to prove our main results using the fixed point theorems, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem; in the end, we are giving two examples to illustrate our results.

Highlights

Differential equations play a very important role in the understanding of qualitative features of many phenomenon and processes in different areas and practical fields
A lot of works have been done concerning these equations in the recent years for their importance in applied sciences; for more details about differential equations and their applications, we refer the readers to [1,2,3,4,5,6,7]
A more general way to describe natural differential equations is through fractional calculus

Summary

Introduction

Differential equations play a very important role in the understanding of qualitative features of many phenomenon and processes in different areas and practical fields. Another important class of differential equations are called pantograph equations, which are a special class of delay differential equations arising in deterministic situations and are of the form This class of differential equations was not properly investigated under fractional derivatives. Initial value problems for pantograph equations with the Hilfer fractional derivative were studied in [22, 27]. To the best of our knowledge, there is no work involving systems of integral boundary value problems for pantograph equations with the Hilfer fractional derivative. The objective of this work is to introduce a new class of coupled systems of Hilfer fractional differential pantograph equations with nonlocal integral boundary conditions of the form 8 >>>>>>

Preliminaries and Notations

Main Results

Examples