International Journal of Differential Equations
Volume 2011 (2011), Article ID 763456, 19 pages
http://dx.doi.org/10.1155/2011/763456
Research Article

Positive Solution to a Fractional Boundary Value Problem

A. Guezane-Lakoud1 and R. Khaldi2

1Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar University, Annaba 23000, Algeria
2Laboratory LASEA, Faculty of Sciences, Badji Mokhtar University, Annaba 23000, Algeria

Received 9 May 2011; Accepted 26 June 2011

Academic Editor: Eduardo Liz

Copyright © 2011 A. Guezane-Lakoud and R. Khaldi. 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

A fractional boundary value problem is considered. By means of Banach contraction principle, Leray-Schauder nonlinear alternative, properties of the Green function, and Guo-Krasnosel'skii fixed point theorem on cone, some results on the existence, uniqueness, and positivity of solutions are obtained.