Analytic and numerical solutions for systems of fractional Schr?dinger equation

摘要

In this work, we address the existence and uniqueness of a fractional system involving nonlinear Schr?dinger equations. This system of fractional partial differential equations arises in quantum mechanics. It describes how the quantum state of some physical system changes with time. We show that the system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The technique is established as an analytic technique of the fixed point theorem. We suppose that all the functions are analytic in the open unit disk. The fractional differential operator is considered from the point of view of the Riemann-Liouville differential operator. Moreover, a numerical scheme for this solution is calculated.