Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation

Huiqin Chen,Yaqiong Cui,Shugui Kang,Caixia Guo,Jianmin Guo,Zhiping Liu

doi:10.1155/2015/206261

Abstract

We investigate the existence of solutions for a Caputo fractional difference equation boundary value problem. We use Schauder fixed point theorem to deduce the existence of solutions. The proofs are based upon the theory of discrete fractional calculus. We also provide some examples to illustrate our main results.

Highlights

The theory of fractional difference equations and their applications have been receiving intensive attention
In [10, 11], the authors studied multiple solutions to fractional difference boundary value problems by means of Krasnosel’skii theorem and Schauder fixed point theorem. They obtained sufficient conditions of the existence of two positive solutions for the boundary value problem of fractional difference equations depending on parameters in [12]
In [14], Kang et al discussed existence of positive solutions for a system of Caputo fractional difference equations depending on parameters on the basis of [13]

Summary

Introduction

The theory of fractional difference equations and their applications have been receiving intensive attention. In [10, 11], the authors studied multiple solutions to fractional difference boundary value problems by means of Krasnosel’skii theorem and Schauder fixed point theorem. They obtained sufficient conditions of the existence of two positive solutions for the boundary value problem of fractional difference equations depending on parameters in [12]. Chen et al [13] presented the existence of at least one positive solution for Caputo fractional boundary value problems.

Results

Conclusion