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Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

Author

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  • Arzu Akbulut
  • Gaetano Luciano

Abstract

The main idea of this study is to obtain the soliton-type solutions of the conformable time-fractional complex Ginzburg–Landau equation with Kerr law nonlinearity. For this aim, the generalized and modified Kudryashov methods are applied to the given model. The reason for using a conformable derivative is that the chain rule can be applied to this derivative. Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. According to our results, both of the used methods are effective and powerful. Finally, 3D and contour plots are given for some results with suitable variables. Our findings in this paper are critical for explaining a wide range of scientific and physical applications. According to our knowledge, our results are new in the literature.

Suggested Citation

  • Arzu Akbulut & Gaetano Luciano, 2023. "Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods," Journal of Mathematics, Hindawi, vol. 2023, pages 1-6, February.
    • Handle: RePEc:hin:jjmath:4741219
    DOI: 10.1155/2023/4741219
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    Cited by:

    1. Nikolay A. Kudryashov & Sofia F. Lavrova, 2023. "Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    2. Arzu Akbulut & Rubayyi T. Alqahtani & Nadiyah Hussain Alharthi, 2023. "Some Latest Families of Exact Solutions to Date–Jimbo–Kashiwara–Miwa Equation and Its Stability Analysis," Mathematics, MDPI, vol. 11(19), pages 1-11, October.

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