General Solutions for the Space-and Time-fractional Diffusion-wave Equation

This paper presents a general solution for a space-and time-fractional diffusionwave equation defined in a bounded space domain. The space-and time-fractional derivatives are described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive a general solution of the space-and time-fractional diffusionwave equation. The solutions of our model equation are calculated in the form of convergent series with easily computable components. Two examples are presented to show the application of the present technique. The effect to varying the order of the time-and space-fractional derivatives on the behaviour of solutions has been investigated. Results show the transition from a pure diffusion process to a pure wave process and the solution continuously depends on the space-fractional derivative.