Uniqueness of positive solutions for boundary value problems of singular fractional differential equations

In this article, we study the existence and uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem D(0+)(alpha)u(t) = f(t, u(t)), 0 < t < 1, u(0) = u(1) = u'(0) = u'(1) = 0, where 3 < alpha <= 4 is a real number, D-0+(alpha) is the Riemann-Liouville fractional derivative and f: (0, 1] x [0, +infinity) is continuous, limt(t) (>0+) f(t, .) = +infinity (i.e. f is singular at t = 0). Our analysis relies on a fixed point theorem in partially ordered sets. As an application, an example is presented to illustrate the main results.