Solutions of the space-time fractional Cattaneo diffusion equation

► In this paper we study the space-time fractional Cattaneo diffusion model. ► The exact solutions of the fractional Cattaneo diffusion equation are obtained. ► From the exact solutions, the fractional order moments are also investigated. ► The long and short time behaviour of the mean square displacement is consistent with the results in A. Compte, R. Metzler, The generalized Cattaneo equation for the description of anomalous transport processes, J. Phys. A: Math. Gen. 30 (1997) 7277-7289.