Duhamel's formula for time‐fractional Schrödinger equations

Abstract

In this paper, we consider the time‐fractional order Schrödinger equation that is a fundamental equation in fractional quantum mechanics. By using the spectral theorem, we prove Duhamel's formula and give some properties of solution operators, which can be used to study the local existence and the global existence of time‐fractional Schrödinger equations on a Hilbert space.