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Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets

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  • Guojie Zheng
  • M. Montaz Ali

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).

Suggested Citation

  • Guojie Zheng & M. Montaz Ali, 2014. "Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, March.
    • Handle: RePEc:hin:jnlaaa:361904
    DOI: 10.1155/2014/361904
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