An Investigation on Reliable Analytical and Numerical Methods for the Riesz Fractional Nonlinear Schrodinger Equation in Quantum Mechanics

In the article, a nonlinear Schrodinger equation with the Riesz fractional derivative has been considered. This equation has been solved by two reliable methods to investigate the accuracy of the solutions. In the implicit finite difference numerical scheme, the fractional centered difference is utilized to approximate the Riesz fractional derivative. Also, a novel modified optimal homotopy asymptotic method with Fourier transform (MOHAM-FT) has been proposed to compute the approximate solution of Riesz fractional nonlinear Schrodinger equation(RFNLSE). Further the numerical solutions of RFNLSE obtained by proposed implicit finite difference method, have been compared with that obtained by MOHAM-FT to exhibit the effectiveness of the suggested methods. Finally, the obtained solutions have been presented graphically to justify the efficiency of the methods.