Positive solutions to a nonlinear three-point boundary value problem with singularity

In this paper, we discuss the existence and uniqueness of positive solutions to a singular boundary value problem of fractional differential equations with three-point integral boundary conditions. The nonlinear term f possesses singularity and also depends on the first-order derivative u′. Our approach is based on Leray-Schauder fixed point theorem and Banach contraction principle. Examples are presented to confirm the application of the main results.

Mathematics Subject Classification. Primary 26A33; Secondary 34B15; 34B18.