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Abstract and Applied Analysis
Volume 2013, Article ID 901625, 12 pages
http://dx.doi.org/10.1155/2013/901625
Research Article

Controllability of Neutral Fractional Functional Equations with Impulses and Infinite Delay

1Department of Mathematics, Anna University, Regional Centre, Coimbatore 641 047, India
2Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
3Department of Mathematics, Anhui Normal University, Wuhu 241000, China
4Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Mersin 10, Turkey

Received 15 March 2013; Accepted 11 July 2013

Academic Editor: Abdelaziz Rhandi

Copyright © 2013 R. Ganesh 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 examine the controllability problem for a class of neutral fractional integrodifferential equations with impulses and infinite delay. More precisely, a set of sufficient conditions are derived for the exact controllability of nonlinear neutral impulsive fractional functional equation with infinite delay. Further, as a corollary, approximate controllability result is discussed by assuming compactness conditions on solution operator. The results are established by using solution operator, fractional calculations, and fixed point techniques. In particular, the controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is controllable. Finally, an example is given to illustrate the obtained theory.