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Solitary Wave Solution of a Generalized Fractional–Stochastic Nonlinear Wave Equation for a Liquid with Gas Bubbles

Author

Listed:
  • Wael W. Mohammed

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

  • Farah M. Al-Askar

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

  • Clemente Cesarano

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

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

In the sense of a conformable fractional operator, we consider a generalized fractional–stochastic nonlinear wave equation (GFSNWE). This equation may be used to depict several nonlinear physical phenomena occurring in a liquid containing gas bubbles. The analytical solutions of the GFSNWE are obtained by using the F-expansion and the Jacobi elliptic function methods with the Riccati equation. Due to the presence of noise and the conformable derivative, some solutions that were achieved are shown together with their physical interpretations.

Suggested Citation

  • Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Mahmoud El-Morshedy, 2023. "Solitary Wave Solution of a Generalized Fractional–Stochastic Nonlinear Wave Equation for a Liquid with Gas Bubbles," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1692-:d:1113752
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    References listed on IDEAS

    as
    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2022. "The Analytical Solutions of the Stochastic mKdV Equation via the Mapping Method," Mathematics, MDPI, vol. 10(22), pages 1-9, November.
    2. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
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