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**Xiaohui Yang**

Department of Computer, Guangdong Police College, Guangzhou, 510230, P. R. China

**Yuji Liu**

Department of Mathematics, Guangdong University of Fiance and Economics,

Guangzhou 510320, P. R. China

This paper is devoted to studying the existence of solutions of two classes of initial value problems for nonlinear fractional differential equations with impulse effects. Firstly we transform initial value problems into integral equations. Then by constructing a special Banach space and employing fixed-point theorem, we obtain some sufficient conditions that guarantee the existence of solutions of these problems of fractional differential equations involving Caputo fractional derivatives. One equation is involved in multiple base points and the other one is involved in a single base point.

- Caputo fractional
- derivative
- fixed-point theorem
- impulsive fractional differential equation
- Initial value problem
- multiple base points FDE
- single base point FDE

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