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International Journal of Differential Equations
Volume 2013 (2013), Article ID 191060, 12 pages
http://dx.doi.org/10.1155/2013/191060
Research Article

An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space

Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

Received 15 April 2013; Accepted 14 July 2013

Academic Editor: Fawang Liu

Copyright © 2013 Asma Bouzaroura and Saïd Mazouzi. 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

This paper is concerned with the existence, uniqueness, and stability of the solution of some impulsive fractional problem in a Banach space subjected to a nonlocal condition. Meanwhile, we give a new concept of a solution to impulsive fractional equations of multiorders. The derived results are based on Banach's contraction theorem as well as Schaefer's fixed point theorem.