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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 104276, 9 pages
http://dx.doi.org/10.1155/2013/104276
Research Article

Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions

1Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology, North Bangkok, Bangkok, Thailand
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 3 June 2013; Accepted 7 August 2013

Academic Editor: Eric R. Kaufmann

Copyright © 2013 Thanin Sitthiwirattham et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a discrete fractional boundary value problem of the form where , , , and is a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented.