Observability estimate for the fractional order parabolic equations on measurable sets. (English) Zbl 1406.93068

Summary: We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain \(\Omega\) of \(\mathbb{R}^n\). The observation region is \(F \times \omega\), where \(\omega\) and \(F\) are measurable subsets of \(\Omega\) and \((0,T)\), 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 [K. D. Phung and G. Wang, J. Eur. Math. Soc. (JEMS) 15, No. 2, 681–703 (2013; Zbl 1258.93037)].


93B07 Observability
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
93C20 Control/observation systems governed by partial differential equations


Zbl 1258.93037
Full Text: DOI


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