Application of Optimal HAM for Solving the Fractional Order Logistic Equation

Mohamed S. Mohamed

doi:doi:10.11648/j.acm.20140301.14

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Application of Optimal HAM for Solving the Fractional Order Logistic Equation

Mohamed S. Mohamed

Published in Applied and Computational Mathematics (Volume 3, Issue 1)

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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APA Style

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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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

Mohamed S. Mohamed

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

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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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download