the matrix transformation technique for the time‎- ‎space fractional linear schrödinger equation

‎this paper deals with a time-space fractional schrödinger equation with homogeneous dirichlet boundary conditions‎. ‎a common strategy for discretizing time-fractional operators is finite difference schemes‎. ‎in these methods‎, ‎the time-step size should usually be chosen sufficiently small‎, ‎and subsequently‎, ‎too many iterations are required which may be time-consuming‎.‎to avoid this issue‎, ‎we utilize the laplace transform method in the present work to discretize time-fractional operators‎. ‎by using the laplace transform‎, ‎the equation is converted to some time-independent problems‎. ‎to solve these problems‎, ‎matrix transformation and improved matrix transformation techniques are used to approximate the spatial derivative terms which are defined by the spectral fractional laplacian operator‎. ‎after solving these stationary equations‎, ‎the numerical inversion of the laplace transform is used to obtain the solution of the original equation‎. ‎the combination of finite difference schemes and the laplace transform creates an efficient and easy-to-implement method for time-space fractional schrödinger equations‎. ‎finally‎, ‎some numerical experiments are presented and show the applicability and accuracy of this approach‎.