An explicit and numerical solutions of the fractional KdV equation

In this paper, a fractional Korteweg-de Vries equation (KdV for short) 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 <= 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. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.