Abstract:

 A class of boundary value problem of fractional differential equation is studied. By the means of the Green′s function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation, and some sufficient conditions on the existence of solution for the boundary value problem are obtained by using Schaefer′s fixed point theorem and Leray-Schauder fixed point theorem. Some known results are extended and improved.

Key words: boundary value problem; fractional differential equation; Caputo fractional derivative; fixed point theorem