Existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditions

In this paper, we discuss the existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditions {CD(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, u ''(0) = u''' (0) = 0, u '(0) = u(1) = eta integral(1)(0) u(s) ds, where 3 < alpha < 4, 0 < eta < 2, D-C(alpha) is the Caputo fractional derivative and f may be singular at u = 0. Our results are based on the Leray- Schauder nonlinear alternative and a fixed-point theorem in cones.