Biccari, Umberto2024-12-122024-12-122022-02Biccari, U. (2022). Internal control for a non-local Schrödinger equation involving the fractional Laplace operator. Evolution Equations and Control Theory, 11(1), 301-324. https://doi.org/10.3934/EECT.20210142163-247210.3934/EECT.2021014http://hdl.handle.net/20.500.14454/2164We analyze the interior controllability problem for a non-local Schrödinger equation involving the fractional Laplace operator (-Δ)s, s ϵ(0 1), on a bounded C1 1 domain  RN. We first consider the problem in one space dimension and employ spectral techniques to prove that, for s ϵ [1/2/1), null-controllability is achieved through an L2(ωX (0,T)) function acting in a subset ω Ω of the domain. This result is then extended to the multi-dimensional case by applying the classical multiplier method, joint with a Pohozaev-type identity for the fractional Laplacian.engFractional LaplacianSchrödinger equationControllabilityPohozaev identityjournal article2024-12-122163-2480