A numerical method for the fractional Schrodinger type equation of spatial dimension two

This work focuses on an investigation of the (n+1)-dimensional time-dependent fractional Schrodinger type equation. In the early part of the paper, the wave function is obtained using Laplace and Fourier transform methods and a symbolic operational form of the solutions in terms of Mittag-Leffler functions is provided. We present an expression for the wave function and for the quantum mechanical probability density. We introduce a numerical method to solve the case where the space component has dimension two. Stability conditions for the numerical scheme are obtained.