Boundary Value Problems
Volume 2011 (2011), Article ID 475126, 17 pages
doi:10.1155/2011/475126
Research Article

Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

Zigen Ouyang,1 Yuming Chen,2 and Shuliang Zou3

1School of Mathematics and Physics, School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
2Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada
3School of Nuclear Science and Technology, University of South China, Hengyang 421001, China

Received 14 November 2010; Accepted 24 February 2011

Academic Editor: Gary Lieberman

Copyright © 2011 Zigen Ouyang 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

Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.