中文摘要：

利用分数阶微积分和不动点定理，给出一类非局部条件下分数阶脉冲微分方程解的定义，并分别在Lipschitz条件和非Lipschitz条件下证明其存在性．

英文摘要：

This paper is concerned with a class of fractional impulsive differential equations, By using fractional calculus and fixed point theorem, the author gives the definition of solutions to the equations and proves the existence of solutions when Lipschitz conditions and non-Lipsehitz conditions are satisfied respectively.