Abstract and Applied Analysis
Volume 2011 (2011), Article ID 986575, 20 pages
http://dx.doi.org/10.1155/2011/986575
Research Article

Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation

Moustafa El-Shahed1 and Wafa M. Shammakh2

1Department of Mathematics, Faculty of Arts and Sciences, College of Education, P.O. Box 3771, Qassim-Unizah 51911, Saudi Arabia
2Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 30903, Jeddah 21487, Saudi Arabia

Received 23 January 2011; Revised 2 April 2011; Accepted 17 April 2011

Academic Editor: Paul Eloe

Copyright © 2011 Moustafa El-Shahed and Wafa M. Shammakh. 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 investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained.