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Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

  • * Corresponding author

    * Corresponding author 

The second author is supported by the Fundamental Research Funds for the Central Universities, China University of Geosciences, Wuhan (No.CUG170627), the Natural Science Foundation of China (NSFC, No.KZ18W30084) and the Hubei NSFC (No.2017CFB279)

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  • This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions on regional gradient exact and approximate controllability are first given and proved in detail. Secondly, we propose an approach on how to calculate the minimum number of $\omega-$strategic actuators. Moreover, the existence, uniqueness and the concrete form of the optimal controller for the system under consideration are presented by employing the Hilbert Uniqueness Method (HUM) among all the admissible ones. Finally, we illustrate our results by an interesting example.

    Mathematics Subject Classification: Primary: 93B05, 35R11; Secondary: 60J60.


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