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On the Solution of the Nonlinear Fractional Diffusion-Wave Equation with Absorption: a Homotopy Approach
Zeitschrift für Naturforschung A2014Vol. 69(3-4), pp. 135–144
Citations Over TimeTop 19% of 2014 papers
Abstract
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.
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