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Abstract and Applied Analysis
Volume 2013, Article ID 301560, 20 pages
http://dx.doi.org/10.1155/2013/301560
Research Article

The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Received 25 April 2013; Accepted 20 June 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Yanan Li 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 boundary value problems for the following nonlinear fractional Sturm-Liouville functional differential equations involving the Caputo fractional derivative: + , , , , , , , where , denote the Caputo fractional derivatives, is a nonnegative continuous functional defined on , , , , are suitably small, , and , . By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively. As an application, an example is presented to illustrate our main results.