Abstract
The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order
α, 0
<
α
⩽
2. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (diffusion-wave) equation. The fractional derivative is described in the Caputo sense. Numerical example is given to show the application of the present technique. Results show the transition from a pure diffusion process (
α
=
1) to a pure wave process (
α
=
2).