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Application of Optimal HAM for Solving the Fractional Order Logistic Equation

Received: 8 December 2013     Published: 28 February 2014
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Abstract

In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of these equations are obtained. The results reveal that this method is very effective and powerful to obtain the approximate solutions.

Published in Applied and Computational Mathematics (Volume 3, Issue 1)
DOI 10.11648/j.acm.20140301.14
Page(s) 27-31
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), 2014. Published by Science Publishing Group

Keywords

Logistic Equation, Fractional Order-Differential Equations, Homotopy Analysis Method, Optimal Value, Caputo's Fractional Derivative

References
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    Mohamed S. Mohamed. (2014). Application of Optimal HAM for Solving the Fractional Order Logistic Equation. Applied and Computational Mathematics, 3(1), 27-31. https://doi.org/10.11648/j.acm.20140301.14

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    ACS Style

    Mohamed S. Mohamed. Application of Optimal HAM for Solving the Fractional Order Logistic Equation. Appl. Comput. Math. 2014, 3(1), 27-31. doi: 10.11648/j.acm.20140301.14

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    AMA Style

    Mohamed S. Mohamed. Application of Optimal HAM for Solving the Fractional Order Logistic Equation. Appl Comput Math. 2014;3(1):27-31. doi: 10.11648/j.acm.20140301.14

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  • @article{10.11648/j.acm.20140301.14,
      author = {Mohamed S. Mohamed},
      title = {Application of Optimal HAM for Solving the Fractional Order Logistic Equation},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {1},
      pages = {27-31},
      doi = {10.11648/j.acm.20140301.14},
      url = {https://doi.org/10.11648/j.acm.20140301.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140301.14},
      abstract = {In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of these equations are obtained. The results reveal that this method is very effective and powerful to obtain the approximate solutions.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Application of Optimal HAM for Solving the Fractional Order Logistic Equation
    AU  - Mohamed S. Mohamed
    Y1  - 2014/02/28
    PY  - 2014
    N1  - https://doi.org/10.11648/j.acm.20140301.14
    DO  - 10.11648/j.acm.20140301.14
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 27
    EP  - 31
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20140301.14
    AB  - In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of these equations are obtained. The results reveal that this method is very effective and powerful to obtain the approximate solutions.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Mathematics Department, Faculty of Science, Al-Azhar University, Egypt;Mathematics Department, Faculty of Science, Taif University, Saudi Arabia

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