Closed Form Solution for the Time-Fractional Schrodinger Equation via Laplace Transform

Abstract

In this work, we apply an efficient technique based on coupling of iterative method and Laplace transform method to obtain the exact solution of the linear and nonlinear time- fractional Schrodinger equations. This method is termed as iterative Laplace transform method. The time-fractional derivative is considered in the Caputo sense and the solutions are found in closed form, in terms of Mittag-Leffler functions. Several numerical examples have been considered to show the effectiveness of the proposed method and the results are compared with the exact solution depicting high accuracy and efficiency.