Numerical solution for the time fractional advection-diffusion-wave model with damping with index 1<γ<2

For three centuries the theory of fractional derivatives developed mainly as a pure theoretical field of mathematics useful only for mathematicians. Fractionalderivatives provide an excellent instrument for the description memory and hereditary properties of various materials and processes. The main advantage of fractional derivatives in comparison with classical integer-order models, become apparent in modeling electrical properties of real materials, aswell as in the description of rheological properties of rocks, and in many other fields. The fractional derivatives are used for modeling phenomena that science has created new electronic developments. In this paper, the time fractional advection-diffusion-wave equation (TFADE) model with damping with index 1 < γ < 2 is considered. By using the implicit numerical method TFADE model convergence is achieved considerably, That finally two numerical examples are expressed.