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A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations

Received: 3 October 2016     Accepted: 5 November 2016     Published: 30 November 2016
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Abstract

In this paper, we present the solution of nonlinear fractional partial differential equations by using the Homotopy Perturbation Aboodh Transform Method (HPATM) and Homotopy Decomposition Method (HDM). The Two methods introduced an efficient tool for solving a wide class of linear and nonlinear fractional differential equations. The results shown that the (HDM) has an advantage over the (HPATM) that it takes less time and using only the inverse operator to solve the nonlinear problems and there is no need to use any other inverse transform as in the case of (HPATM).

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI 10.11648/j.ijtam.20160202.14
Page(s) 45-51
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), 2016. Published by Science Publishing Group

Keywords

Homotopy Decomposition Method, Integral Transforms, Nonlinear Fractional Differential Equation, Aboodh Transform

References
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    Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg. (2016). A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations. International Journal of Theoretical and Applied Mathematics, 2(2), 45-51. https://doi.org/10.11648/j.ijtam.20160202.14

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    Mohand M. Abdelrahim Mahgoub; Abdelilah K. Hassan Sedeeg. A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations. Int. J. Theor. Appl. Math. 2016, 2(2), 45-51. doi: 10.11648/j.ijtam.20160202.14

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    AMA Style

    Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg. A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations. Int J Theor Appl Math. 2016;2(2):45-51. doi: 10.11648/j.ijtam.20160202.14

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  • @article{10.11648/j.ijtam.20160202.14,
      author = {Mohand M. Abdelrahim Mahgoub and Abdelilah K. Hassan Sedeeg},
      title = {A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {2},
      number = {2},
      pages = {45-51},
      doi = {10.11648/j.ijtam.20160202.14},
      url = {https://doi.org/10.11648/j.ijtam.20160202.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.14},
      abstract = {In this paper, we present the solution of nonlinear fractional partial differential equations by using the Homotopy Perturbation Aboodh Transform Method (HPATM) and Homotopy Decomposition Method (HDM). The Two methods introduced an efficient tool for solving a wide class of linear and nonlinear fractional differential equations. The results shown that the (HDM) has an advantage over the (HPATM) that it takes less time and using only the inverse operator to solve the nonlinear problems and there is no need to use any other inverse transform as in the case of (HPATM).},
     year = {2016}
    }
    

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    T1  - A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations
    AU  - Mohand M. Abdelrahim Mahgoub
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    DO  - 10.11648/j.ijtam.20160202.14
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
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    UR  - https://doi.org/10.11648/j.ijtam.20160202.14
    AB  - In this paper, we present the solution of nonlinear fractional partial differential equations by using the Homotopy Perturbation Aboodh Transform Method (HPATM) and Homotopy Decomposition Method (HDM). The Two methods introduced an efficient tool for solving a wide class of linear and nonlinear fractional differential equations. The results shown that the (HDM) has an advantage over the (HPATM) that it takes less time and using only the inverse operator to solve the nonlinear problems and there is no need to use any other inverse transform as in the case of (HPATM).
    VL  - 2
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Author Information
  • Department of Mathematics, Faculty of Science & technology, Omdurman Islamic University, Khartoum, Sudan

  • Mathematics Department Faculty of Education- Holy Quran and Islamic Sciences University, Khartoum, Sudan

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