A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line

Jarunee Soontharanon,Thanin Sitthiwirattham,Saowaluck Chasreechai

doi:10.3390/math7030256

Abstract

In this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder’s fixed point theorem. An example is provided to illustrate the results.

Highlights

Many mathematicians and researchers have extensively studied fractional difference calculus since this subject can be used for describing many problems of real-world phenomena such as mechanical, control systems, flow in porous media, and electrical networks
The basic definitions and properties of fractional difference calculus are given in the book [3]
Sitthiwirattham et al [38] initiated the study of the fractional sum boundary value problem of order

Summary

Introduction

Many mathematicians and researchers have extensively studied fractional difference calculus since this subject can be used for describing many problems of real-world phenomena such as mechanical, control systems, flow in porous media, and electrical networks (see [1,2] and the references therein). Goodrich [22] presented the fractional difference equation of order 1 < α ≤ 2 with a constant boundary condition. Chen and Zhou [29] studied the antiperiodic boundary value problem of order 1 < α ≤ 2. Sitthiwirattham et al [38] initiated the study of the fractional sum boundary value problem of order. Sitthiwirattham [40] proposed the sequential fractional difference equation with the fractional sum boundary condition. The study of coupled systems of fractional differential equations is an important topic in this area (see [48–53] and the references cited therein), and a recent example of the application of systems of fractional difference equations is [54]. For the boundary value problems for systems of discrete fractional equations, there are some studies in this area (see [55–60] and the references cited therein). We present an example to illustrate our result in the last section

Preliminaries

Main Result

Example