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Approximate solutions to time-fractional Schrödinger equation via homotopy analysis method. (English) Zbl 1245.35141
Summary: We construct the approximate solutions of the time-fractional Schrödinger equations, with zero and nonzero trapping potential, by homotopy analysis method (HAM). The fractional derivatives, in the Caputo sense, are used. The method is capable of reducing the size of calculations and handles nonlinear-coupled equations in a direct manner. The results show that HAM is more promising, convenient, efficient and less computational than differential transform method (DTM), and easy to apply in spaces of higher dimensions as well.
MSC:
35R11Fractional partial differential equations
35Q55NLS-like (nonlinear Schrödinger) equations
35A25Other special methods (PDE)