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Entropy 2016, 18(9), 329; doi:10.3390/e18090329

Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation

1
Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221 005, India
2
Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia
3
Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria 0003, South Africa
4
Department of Mathematics, University of Mazandaran, Babolsar 47416, Iran
5
Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 8 July 2016 / Revised: 30 August 2016 / Accepted: 31 August 2016 / Published: 8 September 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
View Full-Text   |   Download PDF [2008 KB, uploaded 8 September 2016]   |  

Abstract

The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various anomalous exponents of particular cases, to predict damping of the field variable. Numerical computations of the convergence control parameter, used to evaluate the convergence of approximate series solution through minimizing error, are also presented graphically for these cases. View Full-Text
Keywords: fractional order system; diffusion-reaction equation; homotopy analysis method; convergence analysis fractional order system; diffusion-reaction equation; homotopy analysis method; convergence analysis
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Tripathi, N.K.; Das, S.; Ong, S.H.; Jafari, H.; Al Qurashi, M. Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation. Entropy 2016, 18, 329.

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