Journal of Applied Mathematics
Volume 2012 (2012), Article ID 931975, 17 pages
http://dx.doi.org/10.1155/2012/931975
Research Article

Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System

Amar Debbouche1 and Dumitru Baleanu2,3

1Department of Mathematics, Faculty of Science, Guelma University, Guelma, Algeria
2Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey
3Institute of Space Sciences, P.O. Box, MG-23, 76900 Magurele-Bucharest, Romania

Received 1 May 2012; Revised 15 July 2012; Accepted 16 July 2012

Academic Editor: F. Marcellán

Copyright © 2012 Amar Debbouche and Dumitru Baleanu. 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 introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.