title: Modified fractional variational iteration method for solving the generalized time-space fractional Schrödinger equation.
abstract: Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.
authors.affiliation: Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China ; Department of Basic Causes, Nanjing Institute of Technology, Nanjing 211167, China.
authors.forename: Baojian
authors.identifier: 0000-0002-4764-3594
authors.initials: B
authors.lastname: Hong
authors.affiliation: Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China.
authors.forename: Dianchen
authors.initials: D
authors.lastname: Lu
mesh_terms: D000465:Algorithms; D008432:Mathematical Computing; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results