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

POSITIVE SOLUTIONS FOR A NONLINEAR FRACTIONAL BOUNDARY VALUE PROBLEM

In this paper, we establish the existence of positive solutions toa nonlinear fractional differential equation with integral boundary conditions.Our approach is based on the linear operator theory and the application ofKrasnosel’skii fixed-point theorem in a cone. We present two examples toillustrate the practicability of our main results