In this paper, linear fractional Schrödinger equation is studied by using compact finite differences method. The fractional part of the equation is worked by applying Caputo fractional derivative definition. In the solution of the problem, finite differences discretization along the time, and fifth-order compact finite differences scheme along the spatial coordinate have been applied. Dispersion analysis is applied to ensure consistency and convergency of the method used. The result shows that the applied method in this study is an applicable technique and approximates the exact solution very well.

non-homogeneous linear fractional Schrödinger equation, homogeneous linear fractional Schrödinger equation, Caputo fractional derivative definition, compact finite differences method, dispersion analysis.