Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation

M. Hafiz Uddin; M. Ali Akbar; Md. Ashrafuzzaman Khan; Md. Abdul Haque

doi:doi:10.11648/j.acm.20170604.13

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Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation

M. Hafiz Uddin, M. Ali Akbar, Md. Ashrafuzzaman Khan, Md. Abdul Haque

Published in Applied and Computational Mathematics (Volume 6, Issue 4)

Received: 21 March 2017 Accepted: 5 April 2017 Published: 14 July 2017

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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].

Published in	Applied and Computational Mathematics (Volume 6, Issue 4)
DOI	10.11648/j.acm.20170604.13
Page(s)	177-184
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Nonlinear Evolution Equation, Fractional Generalized Reaction Duffing Model, Density Dependent Fractional Diffusion Equation, Traveling Wave Solution

References

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APA Style

M. Hafiz Uddin, M. Ali Akbar, Md. Ashrafuzzaman Khan, Md. Abdul Haque. (2017). Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation. Applied and Computational Mathematics, 6(4), 177-184. https://doi.org/10.11648/j.acm.20170604.13

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ACS Style

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. Appl. Comput. Math. 2017, 6(4), 177-184. doi: 10.11648/j.acm.20170604.13

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AMA Style

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. Appl Comput Math. 2017;6(4):177-184. doi: 10.11648/j.acm.20170604.13

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@article{10.11648/j.acm.20170604.13,
  author = {M. Hafiz Uddin and M. Ali Akbar and Md. Ashrafuzzaman Khan and Md. Abdul Haque},
  title = {Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {4},
  pages = {177-184},
  doi = {10.11648/j.acm.20170604.13},
  url = {https://doi.org/10.11648/j.acm.20170604.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170604.13},
  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].},
 year = {2017}
}

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TY  - JOUR
T1  - Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation
AU  - M. Hafiz Uddin
AU  - M. Ali Akbar
AU  - Md. Ashrafuzzaman Khan
AU  - Md. Abdul Haque
Y1  - 2017/07/14
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170604.13
DO  - 10.11648/j.acm.20170604.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 177
EP  - 184
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170604.13
AB  - 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].
VL  - 6
IS  - 4
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

M. Hafiz Uddin, M. Ali Akbar, Md. Ashrafuzzaman Khan, Md. Abdul Haque. (2017). Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation. Applied and Computational Mathematics, 6(4), 177-184. https://doi.org/10.11648/j.acm.20170604.13

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ACS Style

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. Appl. Comput. Math. 2017, 6(4), 177-184. doi: 10.11648/j.acm.20170604.13

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AMA Style

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. Appl Comput Math. 2017;6(4):177-184. doi: 10.11648/j.acm.20170604.13

Copy | Download

@article{10.11648/j.acm.20170604.13,
  author = {M. Hafiz Uddin and M. Ali Akbar and Md. Ashrafuzzaman Khan and Md. Abdul Haque},
  title = {Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {4},
  pages = {177-184},
  doi = {10.11648/j.acm.20170604.13},
  url = {https://doi.org/10.11648/j.acm.20170604.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170604.13},
  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].},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Close Form Solutions of the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation
AU  - M. Hafiz Uddin
AU  - M. Ali Akbar
AU  - Md. Ashrafuzzaman Khan
AU  - Md. Abdul Haque
Y1  - 2017/07/14
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170604.13
DO  - 10.11648/j.acm.20170604.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 177
EP  - 184
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170604.13
AB  - 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].
VL  - 6
IS  - 4
ER  -

Copy | Download