An approximate solution for a fractional diffusion-wave equation using the decomposition method Kamel Al-Khaled a, * ,1 , Shaher Momani b a Department of Mathematics, United Arab Emirates University, Al Maqam Femal Compus, P.O. Box 17551 Al-Ain, UAE b Department of Mathematics, Mutah University, P.O. Box 7 Mutah, Jordan Abstract The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order a,0< a 6 2. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (dif- fusion-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 (a = 1) to a pure wave process (a = 2). Ó 2004 Elsevier Inc. All rights reserved. Keywords: Diffusion-wave equation; Heat equation; Decomposition method; Fractional calculus 0096-3003/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2004.06.026 * Corresponding author. E-mail addresses: kamel.alkhaled@uaeu.ac.ae (K. Al-Khaled), shahermm@yahoo.com (S. Momani). 1 On leave from Department of Mathematics, Jordan University of Science and Technology, IRBID 22110, Jordan. Applied Mathematics and Computation 165 (2005) 473–483 www.elsevier.com/locate/amc