Exact solutions for time-fractional diffusion-wave equations by decomposition method

The time-fractional diffusion-wave equation is considered. The time-fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order alpha is an element of (0, 2]. The fractional derivative is described in the Caputo sense. This paper presents the analytical solutions of the fractional diffusion equations by an Adomian decomposition method. By using initial conditions, the explicit solutions of the equations have been presented in the closed form and then their numerical solutions have been represented graphically. Four examples are presented to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.