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Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method. (English) Zbl 1107.65124
Summary: Based on the symbolic computation system Maple, the Adomian decomposition method, developed for differential equations of integer order, is directly extended to derive explicit and numerical solutions of the fractional Korteweg-de Vries (KdV)-Burgers equation. The fractional derivatives are described in the Caputo sense. According to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional KdV-Burgers equation with time- and space-fractional derivatives. Finally, the solutions of our model equation are calculated in the form of convergent series with easily computable components.

65R20Integral equations (numerical methods)
45K05Integro-partial differential equations
26A33Fractional derivatives and integrals (real functions)
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
68W30Symbolic computation and algebraic computation
Full Text: DOI
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