Volume 6, Issue 4, August 2017, Page: 177-184
Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation
M. Hafiz Uddin, Department of Mathematics, Jessore University of Science and Technology, Jessore, Bangladesh
M. Ali Akbar, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Md. Ashrafuzzaman Khan, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Md. Abdul Haque, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Received: Mar. 21, 2017;       Accepted: Apr. 5, 2017;       Published: Jul. 14, 2017
DOI: 10.11648/j.acm.20170604.13      View  371      Downloads  27
Abstract
The two variable (G'⁄G, 1⁄G)-expansion method is significant for finding the exact traveling wave solution to nonlinear evolution equations (NLEEs) in mathematical physics, applied mathematics and engineering. In this article, we exert the two variable (G'⁄G, 1⁄G)-expansion method for investigating the fractional generalized reaction Duffing model and density dependent fractional diffusion reaction equation and obtain exact solutions containing parameters. When the parameters are taken particular values, traveling wave solutions are transferred into the solitary wave solutions. The two variable (G'⁄G, 1⁄G)-expansion method is the generalization of the original (G'⁄G)-expansion method established by Wang et al [21].
Keywords
Nonlinear Evolution Equation, Fractional Generalized Reaction Duffing Model, Density Dependent Fractional Diffusion Equation, Traveling Wave Solution
To cite this article
M. Hafiz Uddin, M. Ali Akbar, Md. Ashrafuzzaman Khan, Md. Abdul Haque, Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation, Applied and Computational Mathematics. Vol. 6, No. 4, 2017, pp. 177-184. doi: 10.11648/j.acm.20170604.13
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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