Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients

Abstract

Abstract In this paper, by introducing the fractional derivatives in the sense of Caputo, the modified general mapping deformation method (MGMDM) and the modified fractional variational iteration method (MFVIM) are applied to obtain some exact and approximate solutions of the variable-coefficient fractional Schrödinger equation (VFNLS) with time and space fractional derivatives. With the aid of symbolic computation, a broad class of exact analytical solutions and their structure of the VFNLS are investigated. Furthermore, the approximate iterative series showed that the MFVIM is powerful, reliable and effective when compared with some traditional decomposition method in searching for the approximate solutions of the complex nonlinear partial differential equations with variable coefficients and fractional derivatives.

Keywords

• Modified fractional variational iteration method
• Caputo derivative
• Fractional nonlinear Schrödinger equation
• Exact solutions
• Approximate solutions