The asymptotic behavior of the time fractional Schrödinger equation on Hilbert space

The purpose of this article is to show the asymptotic behavior of the solution of the abstract Schrodinger equation with time fractional derivative of order α ∈ (0, 1). We give a detailed description of the long time behavior of the corresponding operator solution. As it is expected in this case, the dynamics are not governed neither by a group nor by a semigroup.