中文摘要：

运用Banach压缩映射原理的推论和广义Lipschitz条件，研究一类阶数在1～2范围内的分数阶微分方程初值问题解的存在性与唯一性，给出该问题存在唯一解的充分条件，推广已有某些结果。

英文摘要：

By using the Banach contraction mapping principle of corollary and generalized Lipschitz conditions,we consider the existence and uniqueness of solution of the initial value problem for a class of fractional differential equations which order within 1 to 2. Sufficient conditions are obtained for the existence and uniqueness of one solution of the problem. Some results in this paper extend the results given in literatures.