The time-fractional Schrodinger equation in the context of non-Markovian dynamics with dissipation

In this paper, we examine the time-fractional Schrodinger equation from the perspective of non-Markovian dynamics in dissipative systems. First, we determine the range of the fractional derivative's order by examining the memory properties of the time-fractional Schrodinger equation. Next, we employ the Jaynes-Cummings model to identify the appropriate mathematical form of the imaginary unit. Finally, we use the refined equation to study quantum teleportation under amplitude damping noise. It was found that the time-fractional Schrodinger equation without fractional operations on the imaginary unit i might be more suitable for describing non-Markovian dynamics in dissipative systems. Our research may provide a new perspective on the time-fractional Schrodinger equation, contributing to a deeper understanding and further development of time-fractional quantum mechanics.