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Efficient techniques for traveling wave solutions of time-fractional Zakharov–Kuznetsov equation

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  • Akram, Ghazala
  • Sadaf, Maasoomah
  • Abbas, Muhammad
  • Zainab, Iqra
  • Gillani, Syeda Rijaa

Abstract

This article manages the development of the traveling wave solutions of time-fractional Zakharov–Kuznetsov (ZK) equation by using the modified auxiliary equation method (MAEM) and analytical approximate solution that is constructed through the residual power series method (RPSM). The MAEM with time fractional beta-derivative is utilized to observe the effects of fractional parameter on the governing model. The RPSM is more useful to retrieve a particular form of wave solution when the initial behavior of the system is known. This method is observed by considering Caputo’s time fractional derivative. Some of the obtained results are graphically illustrated using 3D surface graphs and 2D line plots. The proposed methods are shown to be useful for construction of traveling wave solutions which are hoped to be beneficial in exploring different dynamical behaviors expressed by the equation.

Suggested Citation

  • Akram, Ghazala & Sadaf, Maasoomah & Abbas, Muhammad & Zainab, Iqra & Gillani, Syeda Rijaa, 2022. "Efficient techniques for traveling wave solutions of time-fractional Zakharov–Kuznetsov equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 607-622.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:607-622
    DOI: 10.1016/j.matcom.2021.11.004
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    References listed on IDEAS

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    1. Khaled Moaddy & Mohammed AL-Smadi & Ishak Hashim, 2015. "A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, February.
    2. Abdon Atangana & Emile Franc Doungmo Goufo, 2014. "Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, November.
    3. Lei Fu & Hongwei Yang, 2019. "An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves," Complexity, Hindawi, vol. 2019, pages 1-15, August.
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