Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving  ψ -Hilfer Fractional Derivatives

Athasit Wongcharoen,Sotiris K Ntouyas,Phollakrit Wongsantisuk,Jessada Tariboon,Sergey Shmarev

doi:10.1155/2021/5554619

Abstract

In this article, we discuss the existence and uniqueness of solutions for a new class of coupled system of sequential fractional differential equations involving ψ -Hilfer fractional derivatives, supplemented with multipoint boundary conditions. We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. Examples illustrating the main results are also constructed.

Highlights

Fractional calculus is an emerging field in applied mathematics that deals with derivatives and integrals of arbitrary orders
A generalization of both Riemann-Liouville and Caputo derivatives was given by Hilfer in [7], which is known as the Hilfer fractional derivative Dα,βxðtÞ of order α and a type β ∈ 1⁄20, 1: Some properties and applications of the Hilfer derivative can be found in [8, 9] and references cited therein
In [24], the authors initiated the study of existence and uniqueness of solutions for a new class of boundary value problems of sequential ψ-Hilfer-type fractional differential equations with multipoint boundary conditions of the form

Summary

Introduction

Fractional calculus is an emerging field in applied mathematics that deals with derivatives and integrals of arbitrary orders. In [24], the authors initiated the study of existence and uniqueness of solutions for a new class of boundary value problems of sequential ψ-Hilfer-type fractional differential equations with multipoint boundary conditions of the form 8 >>

Preliminaries

Main Results

Conclusion