Applied and Computational Mathematics

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Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations

Received: 18 May 2013    Accepted:     Published: 30 June 2013
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Abstract

The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM) in this paper. The effectiveness and efficiency of the approximate techniques in handling strongly nonlinear multi-order fractional as well as fractional partial differential equations was established in this paper. It was also shown in this paper that the two approximate techniques employed gave similar results to the considered model equations.

DOI 10.11648/j.acm.20130203.12
Published in Applied and Computational Mathematics (Volume 2, Issue 3, June 2013)
Page(s) 78-85
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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

Homotopy Perturbation Method, Adomian Decomposition Method, Burgers-Poisson Equation, Lie Method, Dispersive Media, Multi-Order Fractional Differential Equations

References
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  • Department of Mathematics, University of Nigeria, Nsukka, 410001, Nigeria

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    Joshua Ikechukwu Nwamba. (2013). Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations. Applied and Computational Mathematics, 2(3), 78-85. https://doi.org/10.11648/j.acm.20130203.12

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    Joshua Ikechukwu Nwamba. Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations. Appl. Comput. Math. 2013, 2(3), 78-85. doi: 10.11648/j.acm.20130203.12

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    AMA Style

    Joshua Ikechukwu Nwamba. Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations. Appl Comput Math. 2013;2(3):78-85. doi: 10.11648/j.acm.20130203.12

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  • @article{10.11648/j.acm.20130203.12,
      author = {Joshua Ikechukwu Nwamba},
      title = {Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations},
      journal = {Applied and Computational Mathematics},
      volume = {2},
      number = {3},
      pages = {78-85},
      doi = {10.11648/j.acm.20130203.12},
      url = {https://doi.org/10.11648/j.acm.20130203.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20130203.12},
      abstract = {The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM)  in this paper. The effectiveness and efficiency of the approximate techniques in handling strongly nonlinear multi-order fractional as well as fractional partial differential equations was established in this paper. It was also shown in this paper that the two approximate techniques employed gave similar results to the considered model equations.},
     year = {2013}
    }
    

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    AB  - The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM)  in this paper. The effectiveness and efficiency of the approximate techniques in handling strongly nonlinear multi-order fractional as well as fractional partial differential equations was established in this paper. It was also shown in this paper that the two approximate techniques employed gave similar results to the considered model equations.
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