Abstract
We study the linear fractional Schrödinger equation on a Hilbert space, with a fractional time derivative of order \(0<\alpha <1,\) and a self-adjoint generator A. Using the spectral theorem we prove existence and uniqueness of strong solutions, and we show that the solutions are governed by an operator solution family \(\{ U_{\alpha }(t)\}_{t\ge 0}\). Moreover, we prove that the solution family \(U_{\alpha }(t)\) converges strongly to the family of unitary operators \(e^{-itA},\) as \(\alpha \) approaches to 1.
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H. Prado and P. Górka enjoyed the support of FONDECYT Grant #1130554, and MECESUP, USA 1298, #596, J. Trujillo has been partially supported the FEDER fund and by Project MTM2013-41704-P from the Government of Spain.
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Górka, P., Prado, H. & Trujillo, J. The Time Fractional Schrödinger Equation on Hilbert Space. Integr. Equ. Oper. Theory 87, 1–14 (2017). https://doi.org/10.1007/s00020-017-2341-6
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DOI: https://doi.org/10.1007/s00020-017-2341-6