Multidimensional problems for general coupled systems of time-space fractional Schrodinger equations

Abstract

In the present paper, general coupled system of nonlinear time-space fractional Schrodinger equations is considered in multi-dimensional case. Finite difference method is used to construct the difference schemes for one and multidimensional problems for general coupled system of nonlinear time-space fractional Schrodinger equations. A reformulation of Grunwald-Letnikov difference derivative is used to construct the difference schemes. Convergence and stability results are presented. Numerical experiments are carried out on problems with one and two dimensional space variables.