The Time Fractional Schrödinger Equation on Hilbert Space

We study the linear fractional Schrödinger equation on a Hilbert space, with a fractional time derivative of order 0 < α< 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 {Uα(t)}t≥0. Moreover, we prove that the solution family Uα(t) converges strongly to the family of unitary operators e- i t A, as α approaches to 1. © 2017, The Author(s).