About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 361904, 5 pages
http://dx.doi.org/10.1155/2014/361904
Research Article

Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2School of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Johannesburg 2050, South Africa
3TCSE, Faculty of Engineering and Built Environment, University of the Witwatersrand (Wits), Johannesburg 2050, South Africa

Received 10 January 2014; Accepted 3 March 2014; Published 27 March 2014

Academic Editor: Sheng-Jie Li

Copyright © 2014 Guojie Zheng and M. Montaz Ali. 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 establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain of . The observation region is , where and are measurable subsets of and (0,), respectively, with positive measure. This inequality is equivalent to the null controllable property for a linear controlled fractional order parabolic equation. The building of this estimate is based on the Lebeau-Robbiano strategy and a delicate result in measure theory provided in Phung and Wang (2013).