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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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1865-7109
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Volume 69, Issue 3-4

Issues

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

Vivek Mishra
  • Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi- 221005, India
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/ Kumar Vishal
  • Department of Mathematics and Basic Science, NIIT University, Neemrana, Rajasthan-301705, India
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/ Subir Das
  • Corresponding author
  • Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi- 221005, India
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/ Seng Huat Ong
Published Online: 2014-06-02 | DOI: https://doi.org/10.5560/zna.2013-0084

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.

Keywords: Fractional Diffusion-Wave Equation; Caputo Derivative; Homotopy Analysis Method

References

    About the article

    Received: 2013-04-04

    Revised: 2013-11-08

    Published Online: 2014-06-02

    Published in Print: 2014-04-01


    Citation Information: Zeitschrift für Naturforschung A, Volume 69, Issue 3-4, Pages 135–144, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.5560/zna.2013-0084.

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