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This paper investigates the regional gradient controllability for ultra-slowdiffusion processes governed by the time fractional diffusion systems with aHadamard-Caputo time fractional derivative. Some necessary and sufficientconditions on regional gradient exact and approximate controllability are firstgiven and proved in detail. Secondly, we propose an approach on how tocalculate the minimum number of $\omega-$strategic actuators. Moreover, theexistence, uniqueness and the concrete form of the optimal controller for thesystem under consideration are presented by employing the Hilbert UniquenessMethod (HUM) among all the admissible ones. Finally, we illustrate our resultsby an interesting example.

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