A new approach for solving the time-fractional Schrödinger equation

The time-fractional Schrödinger equation (TFSE) is a fundamental topic in physics and its numerical solution is still an open problem. In this paper, we propose the reconstruction of variational iteration method (RVIM) for the solution of TFSEs which appear in quantum mechanics. Our method contains an iterative formula that can provide rapidly convergent successive approximations of the exact solution if such a closed form solution exists. Therefore, this method is practical and helpful for solving TFSEs. One numerical example is also reported to confirm the accuracy and efficiency of the presented scheme.