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**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)].

### MSC:

93B07 | Observability |

26A33 | Fractional derivatives and integrals |

35R11 | Fractional partial differential equations |

93C20 | Control/observation systems governed by partial differential equations |

### Citations:

Zbl 1258.93037
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\textit{G. Zheng} and \textit{M. M. Ali}, Abstr. Appl. Anal. 2014, Article ID 361904, 5 p. (2014; Zbl 1406.93068)

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### References:

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