On the Solution of the Nonlinear Fractional Diffusion- Wave Equation with Absorption: a Homotopy Approach

In this article, the homotopy analysis method is used to obtain approximate analytic solutions of the time-fractional diffusion-wave equation with given initial conditions. A special effort has been given to show the effect of reaction term with long term correlation to the diffusion-wave solutions for various values of anomalous exponent to constitute a good mathematical model useful for various engineering and scientific systems. Effects of parameters on the solution profile are calculated numerically and presented through graphs for different particular cases. Sub-diffusion and super-diffusion phenomena for birth and death processes are also shown through figures.