In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Carathéodory 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.

MSC (2010) 26A33, 34B16We investigate the existence of positive solutions to the singular fractional boundary value problem:x, y, z) may be singular at the value 0 of its space variables x, y, z. Here c D stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones.

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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