Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise

In this paper, we establish the existence and uniqueness of the mild solution and the Hölder continuity for the time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise. A full discrete scheme with spectral Galerkin method in space and exponential method in time is proposed. It is rigorously proved that the numerical scheme admits an unique solution. Finally, we present the optimal error estimates of the proposed scheme based on the regularity analysis.