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An explicit and numerical solutions of the fractional KdV equation. (English) Zbl 1119.65394
Summary: A fractional Korteweg-de Vries (KdV) equation with initial condition is introduced by replacing the first order time and space derivatives by fractional derivatives of order $\alpha$ and $\beta$ with $0<\alpha ,\beta \le$ 1, respectively. The fractional derivatives are described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive explicit and numerical solutions of the fractional KdV equation. The solutions of our model equation are calculated in the form of convergent series with easily computable components.
##### MSC:
 65M70 Spectral, collocation and related methods (IVP of PDE) 35Q53 KdV-like (Korteweg-de Vries) equations 26A33 Fractional derivatives and integrals (real functions)