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Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach

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Listed:
  • M. B. Almatrafi

    (Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

Abstract

This research employs the improved modified extended tanh-function technique to explore several solitary wave solutions to the fractional-order Fokas equation. The propagation of waves in fluid dynamics and optical systems are two examples of various natural phenomena that are effectively addressed by the fractional-order Fokas equation. The model captures a generalization of the integer derivative form by including fractional derivatives defined in the conformable sense. We use the phase portrait theory to investigate the existence of traveling wave solutions. The improved modified extended tanh-function technique is successfully applied as a reliable analytical procedure to derive several solitary wave solutions, providing an approachable structure to deal with the complexity introduced by the fractional order. The extracted solutions, which are illustrated by hyperbolic, trigonometric, and rational functions, exhibit a variety of solitary wave shapes, such as bell-shaped, kink, and anti-kink patterns. We additionally evaluate how well the employed method performs in comparison to other approaches. Furthermore, some graphical visualizations are provided to clearly demonstrate the physical behavior of the obtained solutions under various parameter values. The outcomes highlight the effectiveness and adaptability of the proposed strategy in resolving fractional nonlinear differential equations and expand our knowledge of fractional-order systems.

Suggested Citation

  • M. B. Almatrafi, 2024. "Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach," Mathematics, MDPI, vol. 13(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:109-:d:1556415
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    References listed on IDEAS

    as
    1. M. Abu-Shady & Mohammed K. A. Kaabar, 2021. "A Generalized Definition of the Fractional Derivative with Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, October.
    2. Qinghao Zhu & Jianming Qi & Wen-Xiu Ma, 2022. "Exact Solutions of the Nonlinear Space-Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-20, May.
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