Abstract
We provide necessary and sufficient geometric conditions for the exact controllability of the one-dimensional fractional free and fractional harmonic Schrodinger equations. The necessary and sufficient condition for the exact controllability of fractional free Schrodinger equations is derived from the Logvinenko–Sereda theorem and its quantitative version established by Kovrijkine, whereas the one for the exact controllability of fractional harmonic Schrodinger equations is deduced from an infinite dimensional version of the Hautus test for Hermite functions and the Plancherel–Rotach formula.
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