中文摘要：

运用Darbo不动点定理，建立了一类分数阶泛函微分方程初值问题解在L^1[0，1]中存在的充分条件，并通过具体的例子说明了研究结果的应用价值．

英文摘要：

By employing Darbo fixed point theorem, a sufficient condition is established to guarantee the existence of solution for a class of initial value problems of fractional functional differential equations in L^1[0,1] space, an example is also included to illustrate the advantage of the result.