Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems

Chanon Promsakon,Jessada Tariboon,Sotiris K Ntouyas,Feliz Minhós

doi:10.1155/2021/8031524

Abstract

This paper is concerned with the existence and uniqueness of solutions for a new class of boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented with nonlocal integro-multipoint boundary conditions. The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying Schaefer and Krasnoselskii fixed point theorems as well as Leray-Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

Highlights

IntroductionThe fractional calculus has always been an interesting research topic for many years
The fractional calculus has always been an interesting research topic for many years. This is because fractional differential equations describe many real-world process related to memory and hereditary properties of various materials more accurately as compared to classical-order differential equations
We study existence and uniqueness of solutions for boundary value problems for Hilfer-Hadamard fractional differential equations with nonlocal integromultipoint boundary conditions, 8 >>< HHDα1,βxðtÞ = f ðt, xðtÞÞ, t ∈ 1⁄21, T

Summary

Introduction

The fractional calculus has always been an interesting research topic for many years. This is because fractional differential equations describe many real-world process related to memory and hereditary properties of various materials more accurately as compared to classical-order differential equations. Fractional differential equations arise in lots of engineering and clinical disciplines which include biology, physics, chemistry, economics, signal and image processing, and control theory (see the monographs and papers in [1,2,3,4,5,6,7,8]). Various types of fractional derivatives were introduced among which the following Riemann-Liouville and Caputo derivatives are the most widely used ones. For n − 1 < α < n, the derivative of u is

C Dαa uðt Þ

Preliminaries

Main Results

Examples

Conclusion