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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 262191, 10 pages
http://dx.doi.org/10.1155/2013/262191
Research Article

Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

1Department of Mathematics, Guelma University, 24000 Guelma, Algeria
2Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
3Department of Mathematics and Computer Sciences, Cankaya University, 06530 Ankara, Turkey
4Institute of Space Sciences, Magurele, Bucharest, Romania

Received 19 July 2013; Accepted 27 September 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Mourad Kerboua 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 a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.