关键词:  nonlinear fractional differential equation, three-point boundary value problem, positive solutions, green's function, banach contraction mapping, fixed point theorem in cones

Abstract: In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form ... We first transform it into another equivalent boundary value problem. Then, we derive the Green’s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result. 

Key words:  nonlinear fractional differential equation, three-point boundary value problem, positive solutions, green's function, banach contraction mapping, fixed point theorem in cones