We investigate the fractional differential equation) subject to the boundary conditions (0) = 0, (T )+ (T ) = 0. Here α ∈ (1 2), µ ∈ (0 1), is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.
MSC:34A08, 24A33, 34B15