Numerical solutions for fractional KdV–Burgers equation by Adomian decomposition method

Based on the symbolic computation system Maple, Adomian decomposition method, developed for differential equations of integer order, is directly extended to derive explicit and numerical solutions of the fractional 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.