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

Mohand M. Abdelrahim Mahgoub; Abdelilah K. Hassan Sedeeg

doi:doi:10.11648/j.ijtam.20160202.14

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

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

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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ACS 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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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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TY  - JOUR
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
AU  - Abdelilah K. Hassan Sedeeg
Y1  - 2016/11/30
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.14
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
SP  - 45
EP  - 51
PB  - Science Publishing Group
SN  - 2575-5080
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
IS  - 2
ER  -

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Author Information

Mohand M. Abdelrahim Mahgoub

Department of Mathematics, Faculty of Science & technology, Omdurman Islamic University, Khartoum, Sudan
Abdelilah K. Hassan Sedeeg

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

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APA Style

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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ACS 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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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
AU  - Abdelilah K. Hassan Sedeeg
Y1  - 2016/11/30
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.14
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
SP  - 45
EP  - 51
PB  - Science Publishing Group
SN  - 2575-5080
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
IS  - 2
ER  -

Copy | Download