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A Novel (G'/G)-Expansion Method and its Application to the Space-Time Fractional Symmetric Regularized Long Wave (SRLW) Equation

Abstract:

In this work, we use the fractional complex transformation which converts nonlinear fractional partial differential equation to nonlinear ordinary differential equation. A fractional novel (G`/G) - expansion method is used to look for exact solutions of nonlinear evolution equation with the aid of symbolic computation. To check the validity of the method we choose the space-time fractional symmetric regularized long wave (SRLW) equation and as a result, many exact analytical solutions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. The performance of the method is reliable, useful and gives more new general exactsolutions than the existing methods.

Info:

Periodical:

Advanced Trends in Mathematics (Volume 2)

Pages:

1-16

DOI:

https://doi.org/10.18052/www.scipress.com/ATMath.2.1

Citation:

M. Shakeel and S. T. Mohyud-Din, "A Novel (G'/G)-Expansion Method and its Application to the Space-Time Fractional Symmetric Regularized Long Wave (SRLW) Equation", Advanced Trends in Mathematics, Vol. 2, pp. 1-16, 2015

Online since:

March 2015

Authors:

Muhammad Shakeel, Syed Tauseef Mohyud-Din

Keywords:

Exact Solutions, Fractional Partial Differential Equation, Homogeneous Balance, Novel (G'/G)-Expansion Method, Solitary Wave Solutions

Export:

RIS, BibTeX, Text

Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

This article has no references.

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[2] S. Mohyud-Din, S. Bibi, "Exact solutions for nonlinear fractional differential equations using exponential rational function method", Optical and Quantum Electronics, Vol. 49, 2017

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[3] S. ÇULHA ÜNAL, A. DAŞCIOĞLU, D. VAROL BAYRAM, "Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation", Mathematical Sciences and Applications E-Notes, p. 53, 2021

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[4] S. Yao, T. Rasool, R. Hussain, H. Rezazadeh, M. Inc, "Exact soliton solutions of conformable fractional coupled Burger’s equation using hyperbolic funtion approach", Results in Physics, p. 104776, 2021

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[5] S. Yao, T. Rasool, R. Hussain, H. Rezazadeh, M. Inc, "Exact soliton solutions of conformable fractional coupled Burger’s equation using hyperbolic funtion approach", Results in Physics, Vol. 30, p. 104776, 2021

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[6] S. Yao, T. Rasool, R. Hussain, H. Rezazadeh, M. Inc, "Exact soliton solutions of conformable fractional coupled Burger’s equation using hyperbolic funtion approach", Results in Physics, Vol. 30, p. 104776, 2021

DOI: https://doi.org/10.1016/j.rinp.2021.104776

[7] S. Yao, T. Rasool, R. Hussain, H. Rezazadeh, M. Inc, "Exact soliton solutions of conformable fractional coupled Burger’s equation using hyperbolic funtion approach", Results in Physics, Vol. 30, p. 104776, 2021

DOI: https://doi.org/10.1016/j.rinp.2021.104776

[8] S. Yao, T. Rasool, R. Hussain, H. Rezazadeh, M. Inc, "Exact soliton solutions of conformable fractional coupled Burger’s equation using hyperbolic funtion approach", Results in Physics, Vol. 30, p. 104776, 2021

DOI: https://doi.org/10.1016/j.rinp.2021.104776

[9] S. Yao, T. Rasool, R. Hussain, H. Rezazadeh, M. Inc, "Exact soliton solutions of conformable fractional coupled Burger’s equation using hyperbolic funtion approach", Results in Physics, Vol. 30, p. 104776, 2021

DOI: https://doi.org/10.1016/j.rinp.2021.104776

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[15] S. Mohanty, O. Kravchenko, A. Dev, "Exact traveling wave solutions of the Schamel Burgers’ equation by using generalized-improved and generalized G′G expansion methods", Results in Physics, Vol. 33, p. 105124, 2022

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[16] S. Mohanty, O. Kravchenko, A. Dev, "Exact traveling wave solutions of the Schamel Burgers’ equation by using generalized-improved and generalized G′G expansion methods", Results in Physics, Vol. 33, p. 105124, 2022

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[19] S. Mohanty, S. Kumar, A. Dev, M. Deka, D. Churikov, O. Kravchenko, "An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients", Results in Physics, p. 105504, 2022

DOI: https://doi.org/10.1016/j.rinp.2022.105504

[20] S. Mohanty, S. Kumar, A. Dev, M. Deka, D. Churikov, O. Kravchenko, "An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients", Results in Physics, p. 105504, 2022

DOI: https://doi.org/10.1016/j.rinp.2022.105504

[21] S. Mohanty, S. Kumar, A. Dev, M. Deka, D. Churikov, O. Kravchenko, "An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients", Results in Physics, Vol. 37, p. 105504, 2022

DOI: https://doi.org/10.1016/j.rinp.2022.105504

[22] Q. Zhu, J. Qi, W. Ma, "Exact Solutions of the Nonlinear Space-Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods", Advances in Mathematical Physics, Vol. 2022, p. 1, 2022

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[23] S. Mohanty, S. Kumar, A. Dev, M. Deka, D. Churikov, O. Kravchenko, "An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients", Results in Physics, Vol. 37, p. 105504, 2022

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[24] S. Mohanty, S. Kumar, A. Dev, M. Deka, D. Churikov, O. Kravchenko, "An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients", Results in Physics, Vol. 37, p. 105504, 2022

DOI: https://doi.org/10.1016/j.rinp.2022.105504

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