Iterative Positive Solutions to a Coupled Hadamard-Type Fractional Differential System on Infinite Domain with the Multistrip and Multipoint Mixed Boundary Conditions

Xinran Du,Huihui Pang,Yuan Meng

doi:10.1155/2020/6508075

Abstract

This paper is devoted to the existence of positive solutions for a nonlinear coupled Hadamard fractional differential system, with multistrip and multipoint mixed boundary conditions on an infinite interval. Based on the Arzelá-Ascoli theorem, we establish an important lemma to prove the complete continuity of operators on the infinite interval. Using the monotone iterative technique, the existence criteria for positive extremal solutions can be acquired, and an example is given to illustrate the feasibility of the above study as well.

Highlights

Fractional calculus, which is organically united with integral calculus, extends the concept of classical integral calculus to the whole real number line and even the complex plane
The study of differential equations with fractional calculus is of significance theoretically and practically
Inspired by the aforementioned work, to get more extensive results, we investigate the existence of iterative positive solutions to the following Hadamard fractional differential systems

Summary

Introduction

Fractional calculus, which is organically united with integral calculus, extends the concept of classical integral calculus to the whole real number line and even the complex plane. Inspired by the aforementioned work, to get more extensive results, we investigate the existence of iterative positive solutions to the following Hadamard fractional differential systems. The main aim of this paper is to investigate the coupled nonlinear fractional differential system of the Hadamard type on infinite intervals subject to the coupled multistrip and multipoint mixed boundary conditions. This kind of condition is a linear combination of values at the multiple band integrals and the different discrete points, which highly summarizes the characteristics of boundary conditions in the existing study. The main results are illustrated by a practical example

Preliminaries

Γðα1ÞΓðα2Þ

Existence Results of Monotone Iterative Positive Solutions