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On the regional gradient observability of time fractional diffusion processes. (English) Zbl 1348.93054

Summary: This paper for the first time addresses the concepts of regional gradient observability for the Riemann-Liouville time fractional order diffusion system in an interested subregion of the whole domain without the knowledge of the initial vector and its gradient. The Riemann-Liouville time fractional order diffusion system which replaces the first order time derivative of normal diffusion system by a Riemann-Liouville time fractional order derivative of order \(\alpha \in(0, 1]\) is used to well characterize those anomalous sub-diffusion processes. The characterizations of the strategic sensors when the system under consideration is regional gradient observable are explored. We then describe an approach leading to the reconstruction of the initial gradient in the considered subregion with zero residual gradient vector. At last, to illustrate the effectiveness of our results, we present several application examples where the sensors are zone, pointwise or filament ones.

MSC:

93B07 Observability
93C20 Control/observation systems governed by partial differential equations
35R11 Fractional partial differential equations
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