一类分数阶微分方程边值问题解的存在性

Existence of solution for the boundary value problem of a class of fractional differential equation

研究了一类分数阶微分方程边值问题。应用Green函数,将分数阶微分方程边值问题转化为等价的积分方程,利用Schaefer不动点定理和Leray-Schauder不动点定理得到了该边值问题存在解的充分条件,推广和完善了已有的结果。

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.