Applied and Computational Mathematics

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

Received: Mar. 21, 2017    Accepted: Apr. 05, 2017    Published: Jul. 14, 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].

DOI 10.11648/j.acm.20170604.13
Published in Applied and Computational Mathematics (Volume 6, Issue 4, August 2017)
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), 2024. 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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Author Information
  • Department of Mathematics, Jessore University of Science and Technology, Jessore, Bangladesh

  • Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

  • Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

  • Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

Cite This Article
  • 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://download.sciencepg.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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    AU  - M. Ali Akbar
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    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
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