Advances in Difference Equations
Volume 2011 (2011), Article ID 546038, 14 pages
doi:10.1155/2011/546038
Research Article

The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions

Meiqiang Feng,1 Xiaofang Liu,1 and Hanying Feng2

1School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
2Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 19 December 2010; Accepted 26 January 2011

Academic Editor: J. J. Trujillo

Copyright © 2011 Meiqiang Feng 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

The expression and properties of Green's function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.