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The Optical Solutions of the Stochastic Fractional Kundu–Mukherjee–Naskar Model by Two Different Methods

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  • 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)

  • 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, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

  • M. El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

In this paper, we focus on the stochastic fractional Kundu–Mukherjee–Naskar equation perturbed in the Stratonovich sense by the multiplicative Wiener process. To gain new elliptic, rational, hyperbolic and trigonometric stochastic solutions, we use two different methods: the Jacobi elliptic function method and the ( G ′ / G ) -expansion method. Because of the significance of the Kundu-Mukherjee equation in a magnetized plasma, the obtained solutions are useful in understanding many remarkable physical phenomena. Furthermore, we show the effect of the multiplicative Wiener process on the obtained solutions of the Kundu–Mukherjee–Naskar equation.

Suggested Citation

  • Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2022. "The Optical Solutions of the Stochastic Fractional Kundu–Mukherjee–Naskar Model by Two Different Methods," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1465-:d:803461
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    References listed on IDEAS

    as
    1. Mijena, Jebessa B. & Nane, Erkan, 2015. "Space–time fractional stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3301-3326.
    2. Iqbal, Naveed & Wu, Ranchao & Mohammed, Wael W., 2021. "Pattern formation induced by fractional cross-diffusion in a 3-species food chain model with harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 102-119.
    3. Wael W. Mohammed & Meshari Alesemi & Sahar Albosaily & Naveed Iqbal & M. El-Morshedy, 2021. "The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation by Using ( G ′ G )-Expansion Method," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
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