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). © 2004 Elsevier Inc. All rights reserved.