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Solutions to the (4+1)-Dimensional Time-Fractional Fokas Equation with M-Truncated Derivative

Author

Listed:
  • Wael W. Mohammed

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Farah M. Al-Askar

    (Department of Mathematical Science, Collage of Science, Princess Nourah Bint, Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

In this paper, we consider the (4+1)-dimensional fractional Fokas equation (FFE) with an M-truncated derivative. The extended tanh–coth method and the Jacobi elliptic function method are utilized to attain new hyperbolic, trigonometric, elliptic, and rational fractional solutions. In addition, we generalize some previous results. The acquired solutions are beneficial in analyzing definite intriguing physical phenomena because the FFE equation is crucial for explaining various phenomena in optics, fluid mechanics and ocean engineering. To demonstrate how the M-truncated derivative affects the analytical solutions of the FFE, we simulate our figures in MATLAB and show several 2D and 3D graphs.

Suggested Citation

  • Wael W. Mohammed & Clemente Cesarano & Farah M. Al-Askar, 2022. "Solutions to the (4+1)-Dimensional Time-Fractional Fokas Equation with M-Truncated Derivative," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:194-:d:1019732
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    References listed on IDEAS

    as
    1. Sheng Zhang & Meitong Chen, 2015. "Painlevé Integrability and New Exact Solutions of the (4 + 1)-Dimensional Fokas Equation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, December.
    2. Wael W. Mohammed & Mohammed Alshammari & Clemente Cesarano & Sultan Albadrani & M. El-Morshedy, 2022. "Brownian Motion Effects on the Stabilization of Stochastic Solutions to Fractional Diffusion Equations with Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-9, April.
    3. Yinghui He, 2014. "Exact Solutions for -Dimensional Nonlinear Fokas Equation Using Extended F -Expansion Method and Its Variant," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, April.
    4. Wael W. Mohammed & Naveed Iqbal, 2022. "Impact Of The Same Degenerate Additive Noise On A Coupled System Of Fractional Space Diffusion Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-14, February.
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