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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 502839, 9 pages
http://dx.doi.org/10.1155/2013/502839
Research Article

Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces

Eastern Mediterranean University, Gazimagusa, T.R. North Cyprus, Mersin 10, Turkey

Received 3 January 2013; Accepted 1 February 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 N. I. Mahmudov. 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 discuss the approximate controllability of semilinear fractional Sobolev-type differential system under the assumption that the corresponding linear system is approximately controllable. Using Schauder fixed point theorem, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional Sobolev-type differential equations, are formulated and proved. We show that our result has no analogue for the concept of complete controllability. The results of the paper are generalization and continuation of the recent results on this issue.