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Herzallah, Mohamed A. E.; Gepreel, Khaled A.

Approximate solution to the time-space fractional cubic nonlinear Schrödinger equation. (English) Zbl 1254.65115

Appl. Math. Modelling 36, No. 11, 5678-5685 (2012).
Summary: By introducing the fractional derivatives in the sense of Caputo, we use the Adomian decomposition method to construct the approximate solutions for the cubic nonlinear fractional Schrödinger equation with time and space fractional derivatives. The exact solution of the cubic nonlinear Schrödinger equation is given as a special case of our approximate solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equation.

Cited in 32 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q55 NLS equations (nonlinear Schrödinger equations)
35R11 Fractional partial differential equations

Keywords:

Adomian decomposition method; fractional calculus; cubic nonlinear fractional Schrödinger equation
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\textit{M. A. E. Herzallah} and \textit{K. A. Gepreel}, Appl. Math. Modelling 36, No. 11, 5678--5685 (2012; Zbl 1254.65115)
Full Text: DOI

References:

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