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Mathematical Problems in Engineering
Volume 2015, Article ID 519072, 8 pages
http://dx.doi.org/10.1155/2015/519072
Research Article

On Nonlinear Fractional Sum-Difference Equations via Fractional Sum Boundary Conditions Involving Different Orders

Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Received 13 July 2015; Revised 3 September 2015; Accepted 6 September 2015

Academic Editor: Sotiris K. Ntouyas

Copyright © 2015 Saowaluk Chasreechai 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 study existence and uniqueness results for Caputo fractional sum-difference equations with fractional sum boundary value conditions, by using the Banach contraction principle and Schaefer’s fixed point theorem. Our problem contains different numbers of order in fractional difference and fractional sums. Finally, we present some examples to show the importance of these results.