Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problem D-0+(alpha) u(t) + f(t, u(t)) = 0,0 < 1, u(0) = u'(0) = u ''(0) = 0, u ''(1) = beta u ''(eta), where 3 < alpha <= 4, D-0+(alpha) is the standard Riemann-Liouville derivative and f : (0, 1] x [0, infinity) -> [0, infinity) with limt(t -> 0+) f(t, center dot) = infinity i.e., f is singular at t = 0). Our analysis relies on a fixed point theorem in partially ordered metric spaces.