Series solutions for nonlinear time-fractional Schrödinger equations: Comparisons between conformable and Caputo derivatives

Abstract

In the present paper, we present the exact analytical solution of the time-fractional Schrödinger equation (TFSE) in the sense of conformable fractional derivative (Co-FD) based on the residual power series method (RPSM). Moreover, we make graphical comparisons between the solution of this problem in the sense of Co-FD and the obtained solutions in previous studied in the sense of Caputo fractional derivative (Ca-FD). Comparisons indicate that Co-FD is a suitable alternative to Ca-FD in the modeling of TFSE. The main advantage for employing the RPSM is the simplicity of computing the coefficients of the series solution by applying differential operators without having to use integrated operators. Finally, our proposed technique can be applied easily in the solution of higher dimension without any restriction on the type of equation and the Co-FD can be used to formulate other types of partial differential equation.