The <i>G'/G<sup>2</sup></i> - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations

Abaker A. Hassaballa

doi:doi:10.11648/j.acm.20200903.12

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The G'/G² - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations

Abaker A. Hassaballa

Published in Applied and Computational Mathematics (Volume 9, Issue 3)

Received: 18 April 2020 Accepted: 12 May 2020 Published: 27 May 2020

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Abstract

In this paper, we apply G’/G²-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’s modified Riemann-Liouville fractional derivative. The travelling wave solution is approximated by the G’/G²-Expansion method with unknown parameters that can be expressed by trigonometric functions, exponential functions, hyperbolic functions and rational functions. These results reveal that the proposed method is very effective and simple in performing a solution to the nonlinear fractional partial differential equation.

Published in	Applied and Computational Mathematics (Volume 9, Issue 3)
DOI	10.11648/j.acm.20200903.12
Page(s)	56-63
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), 2020. Published by Science Publishing Group

Keywords

G’/G²-expansion Method, Burgers-Fisher Equation, Burgers Equation

References

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[3]	Saleh Alshammari, Mohammed Al-Smadi, Mohammad Al Shammari, Ishak Hashim, and Mohd Almie Alias, (2019). Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions. International journal of differential equations, vol. 2019, pp. 1-11.
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[5]	Cheng Chen and Yao-Lin Jiang, (2018). Simplest equation method for some time-fractional partial differential equations with conformable derivative. Computers and Mathematics with Applications, vol. 75, Issue 8, pp. 2978-2988.
[6]	E. A. Yousif, E. A-B. Abdel-Salam, M. A. El-Aasser, (2018). On the solution of the space-time fractional cubic nonlinear Schrödinger equation. Elsevier, Results in Physics, vol. 8, pp. 702-708.
[7]	M. Alaroud, M. Al-Smadi, R. R. Ahmad, and U. K. Salma Din, (2018). Computational optimization of residual power series algorithm for certain classes of fuzzy fractional differential equations. International journal of differential Equations, vol. 2018, pp. 1-11.
[8]	M. Ali Akbar, Norhashidah Hj. Mohd. Ali, Ripan Roy, (2018). Closed form solutions of two time fractional nonlinear wave equations. Elsevier, Results in Physics, vol. 9, pp. 1031-1039.
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[10]	Arzu Akbulut a and Melike Kaplan, (2018). Auxiliary equation method for time-fractional differential equations with conformable derivative. Computers and Mathematics with Applications, vol. 75, Issue 3, pp. 876-882.
[11]	Dazhi Zhao. Maokang Luo (2017). General conformable fractional derivative and its physical interpretation. Springer-Verlag Italia, 54, pp. 903–917.
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Abaker A. Hassaballa. (2020). The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations. Applied and Computational Mathematics, 9(3), 56-63. https://doi.org/10.11648/j.acm.20200903.12

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ACS Style

Abaker A. Hassaballa. The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations. Appl. Comput. Math. 2020, 9(3), 56-63. doi: 10.11648/j.acm.20200903.12

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AMA Style

Abaker A. Hassaballa. The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations. Appl Comput Math. 2020;9(3):56-63. doi: 10.11648/j.acm.20200903.12

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@article{10.11648/j.acm.20200903.12,
  author = {Abaker A. Hassaballa},
  title = {The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {3},
  pages = {56-63},
  doi = {10.11648/j.acm.20200903.12},
  url = {https://doi.org/10.11648/j.acm.20200903.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200903.12},
  abstract = {In this paper, we apply G’/G2-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’s modified Riemann-Liouville fractional derivative. The travelling wave solution is approximated by the G’/G2-Expansion method with unknown parameters that can be expressed by trigonometric functions, exponential functions, hyperbolic functions and rational functions. These results reveal that the proposed method is very effective and simple in performing a solution to the nonlinear fractional partial differential equation.},
 year = {2020}
}

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TY  - JOUR
T1  - The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations
AU  - Abaker A. Hassaballa
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200903.12
DO  - 10.11648/j.acm.20200903.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 56
EP  - 63
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200903.12
AB  - In this paper, we apply G’/G2-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’s modified Riemann-Liouville fractional derivative. The travelling wave solution is approximated by the G’/G2-Expansion method with unknown parameters that can be expressed by trigonometric functions, exponential functions, hyperbolic functions and rational functions. These results reveal that the proposed method is very effective and simple in performing a solution to the nonlinear fractional partial differential equation.
VL  - 9
IS  - 3
ER  -

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Author Information

Abaker A. Hassaballa

Department of Mathematics, College of Applied & Industrial Sciences, Bahri University, Khartoum, Sudan

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Abaker A. Hassaballa. (2020). The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations. Applied and Computational Mathematics, 9(3), 56-63. https://doi.org/10.11648/j.acm.20200903.12

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ACS Style

Abaker A. Hassaballa. The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations. Appl. Comput. Math. 2020, 9(3), 56-63. doi: 10.11648/j.acm.20200903.12

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AMA Style

Abaker A. Hassaballa. The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations. Appl Comput Math. 2020;9(3):56-63. doi: 10.11648/j.acm.20200903.12

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@article{10.11648/j.acm.20200903.12,
  author = {Abaker A. Hassaballa},
  title = {The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {3},
  pages = {56-63},
  doi = {10.11648/j.acm.20200903.12},
  url = {https://doi.org/10.11648/j.acm.20200903.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200903.12},
  abstract = {In this paper, we apply G’/G2-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’s modified Riemann-Liouville fractional derivative. The travelling wave solution is approximated by the G’/G2-Expansion method with unknown parameters that can be expressed by trigonometric functions, exponential functions, hyperbolic functions and rational functions. These results reveal that the proposed method is very effective and simple in performing a solution to the nonlinear fractional partial differential equation.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - The G'/G2 - Expansion Method for Solving Fractional Burgers - Fisher and Burgers Equations
AU  - Abaker A. Hassaballa
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200903.12
DO  - 10.11648/j.acm.20200903.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 56
EP  - 63
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200903.12
AB  - In this paper, we apply G’/G2-Expansion method to discover a strategy for the approximate solution of the generalized fractional Burger-Fisher equation and fractional Burger equation. The given fractional Burger-Fisher and burger equation through substitution are converted into nonlinear ordinary differential equations, in the sense of the Jumarie’s modified Riemann-Liouville fractional derivative. The travelling wave solution is approximated by the G’/G2-Expansion method with unknown parameters that can be expressed by trigonometric functions, exponential functions, hyperbolic functions and rational functions. These results reveal that the proposed method is very effective and simple in performing a solution to the nonlinear fractional partial differential equation.
VL  - 9
IS  - 3
ER  -

Copy | Download