|
Z. Naturforsch. 69a, 135 – 144
(2014)
doi:10.5560/ZNA.2013-0084
On the Solution of the Nonlinear Fractional Diffusion-Wave Equation with Absorption: a Homotopy Approach
1 Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi-221005, India
2 Department of Mathematics and Basic Science, NIIT University, Neemrana, Rajasthan-301705, India
3 Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur-50603, Malaysia
Received April 4, 2013 / revised November 8, 2013 / published online January 22, 2014
Reprint requests to: S. D.; E-mail:
subir_das08@hotmail.com
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.
Key words: Fractional Diffusion-Wave Equation; Caputo Derivative; Homotopy Analysis Method.
Mathematics Subject Classification 2000: 26A33; 34A08; 60G22; 65Gxx; 35R11