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Advances in Mathematical Physics
Volume 2016, Article ID 7307614, 9 pages
http://dx.doi.org/10.1155/2016/7307614
Research Article

Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application

School of Mathematics and Computer Sciences, Shanxi Datong University, Shanxi, Datong 037009, China

Received 13 February 2016; Accepted 5 April 2016

Academic Editor: Ivan Avramidi

Copyright © 2016 Caixia Guo 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

This paper is concerned with the two-point boundary value problems of nonlinear finite discrete fractional differential equations. On one hand, we discuss some new properties of the Green function. On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.