Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion–wave equations

In this paper, the Laplace decomposition method is employed to obtain approximate analytical solutions of the linear and nonlinear fractional diffusion–wave equations. This method is a combined form of the Laplace transform method and the Adomian decomposition method. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. The fractional derivative described here is in the Caputo sense. Some illustrative examples are presented and the results show that the solutions obtained by using this technique have close agreement with series solutions obtained with the help of the Adomian decomposition method.