一类Caputo分数阶微分方程初值问题解的存在性

Existence of solutions of initial value problem for a Caputo fractional differential equation

将一类Caputo分数阶微分方程初值问题转化为等价的Volterra积分方程,通过构造一个特殊的Banach空间,在此Banach空间上定义算子,将求解Volterra积分方程转化为求算子的不动点问题,应用Schauder不动点定理证明了其解的存在性.

The initial value problem of a class of Caputo fractional differential equations is trans‐formed into an equivalent Volterra integral equation .By defining a operator on a special Banach space ,the solvability of the Volterra integral equation is transformed to a fixed point problem . The existence of its solution is proved by employing Schauder′s fixed point theorem .