Positive solutions for Dirichlet problems, of singular nonlinear fractional differential equations

In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: D(alpha)u(t) + f (t, u(t), D-mu u(t)) = 0, u(0) = u(1) = 0, where 1 < alpha < 2, 0 < mu <= alpha - 1, D-alpha is the standard Riemann-Liouville fractional derivative, f is a positive Caratheodory function and f (t, x, y) is singular at x = 0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques. (C) 2010 Elsevier Inc. All rights reserved.