Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 914592, 9 pages
Research Article

The Solvability and Optimal Controls for Some Fractional Impulsive Equation

1School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China
2College of Sciences, Guangxi University for Nationalities Nanning, Guangxi 530006, China
3Faculty of Mathematics and Computer Science, Jagiellonian University, ul. S. Lojasiewicza 6, 30-348 Krakow, Poland

Received 21 April 2013; Revised 18 June 2013; Accepted 27 July 2013

Academic Editor: Naseer Shahzad

Copyright © 2013 Xianghu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.