Abstract
Abstract This paper is devoted to the investigation of regional controllability of the fractional order sub-diffusion process. We first derive the equivalent integral equations of the abstract sub-diffusion systems with Caputo and Riemann-Liouville fractional derivatives by utilizing the Laplace transform. The new definitions of regional controllability of the system studied are introduced by extending the existence contributions. Then we analyze the regional controllability of the fractional order sub-diffusion system with minimum energy control in two different cases: B ∈ L $\mathcal{L}$ (R m , L 2(Ω)). T he adjoint system of fractional order sub-diffusion system is also presented at the same time. Two applications are worked out in the end to verify the effectiveness of our results.
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