一类分数阶微分方程边值问题解的存在性

Existence of Solutions to a Boundary Value Problem of Fractional Differential Equations

将一类分数阶微分方程边值问题转化为等价的积分方程,通过构造特殊的Banach空间,应用Kuratowski非紧性测度的性质及Darbo不动点定理,得到了在无穷区间上分数阶微分方程解的存在性结果,并通过具体例子说明了主要结果.

The existence of solutions to a boundary value problem of fractional differential equations on the half-axis in a Banach space was studied.The boundary value problem was transformed into an equivalent integral equation.By the properties of the Kuratowski noncompactness measure and Darbo＇s fixed point theorem, the existence of solutions of boundary value problem were proved.An example illustrating the main result was also given.