关键词: fractional differential equation, positive solution, fixed point theorem

Abstract: In this paper, we discuss a singular system of nonlinear fractional differential equation, in which the inhomogeneous term depends on the fractional derivative of lower order. By using the Krasnoselskii’s fixed point theorem and the Leray-Schauder nonlinear alternative method, some sufficient conditions for the existence of positive solution of the singular system are obtained.

Key words: fractional differential equation, positive solution, fixed point theorem