Solving Time Fractional Schrödinger Equation in the Sense of Local Fractional Derivative

Abstract

The motivation of the study is solving the mathematical problems including time fractional Schrödinger equation by means of a method which is a combination of Chebyshev collocation method and residual power series method (RPSM). The time fractional derivative in local fractional derivative sense is discretized with the help of Chebyshev collocation method to reduce time fractional Schrödinger equation into a system including two fractional ordinary differential equations. At this stage, applying RPSM produces the truncated solution of the mathematical problem. Given examples illustrated that this method is applicable and compatible for solving mathematical problems with fractional derivative.