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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 142067, 9 pages
http://dx.doi.org/10.1155/2014/142067
Research Article

The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order

1School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China
2Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China
3College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, China

Received 3 August 2013; Revised 17 October 2013; Accepted 8 November 2013; Published 28 January 2014

Academic Editor: Stanislaw Migorski

Copyright © 2014 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.

Abstract

We study the existence of solutions and optimal controls for some fractional impulsive equations of order . By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results.