Abstract and Applied Analysis
Volume 2011 (2011), Article ID 605614, 9 pages
http://dx.doi.org/10.1155/2011/605614
Research Article

Existence Results for Singular Boundary Value Problem of Nonlinear Fractional Differential Equation

Yujun Cui

Department of Mathematics, Shandong University of Science and Technology, Qingdao 266510, China

Received 27 December 2010; Revised 2 March 2011; Accepted 3 March 2011

Academic Editor: Elena Braverman

Copyright © 2011 Yujun Cui. 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

By applying a fixed point theorem for mappings that are decreasing with respect to a cone, this paper investigates the existence of positive solutions for the nonlinear fractional boundary value problem: 𝐷 𝛼 0 + 𝑢 ( 𝑡 ) + 𝑓 ( 𝑡 , 𝑢 ( 𝑡 ) ) = 0 , 0 < 𝑡 < 1 , 𝑢 ( 0 ) = 𝑢 ′ ( 0 ) = 𝑢 ′ ( 1 ) = 0 , where 2 < 𝛼 < 3 , 𝐷 𝛼 0 + is the Riemann-Liouville fractional derivative.