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Impact of Multiplicative Noise on the Exact Solutions of the Fractional‐Stochastic Boussinesq‐Burger System

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  • Wael W. Mohammed
  • Farah M. Al-Askar
  • M. El-Morshedy

Abstract

In this paper, we consider the fractional‐stochastic Boussinesq‐Burger system (FSBBS) generated by the multiplicative Brownian motion. The Jacobi elliptic function techniques are used to create creative elliptic, hyperbolic, and rational fractional‐stochastic solutions for FSBBS. Furthermore, we draw 2D and 3D graphs by using the MATLAB Package for some obtained solutions of FSBBS to discuss the influence of the Brownian motion on these solutions. Finally, we indicate that the Brownian motion stabilizes the solutions of FSBBS around zero.

Suggested Citation

  • Wael W. Mohammed & Farah M. Al-Askar & M. El-Morshedy, 2022. "Impact of Multiplicative Noise on the Exact Solutions of the Fractional‐Stochastic Boussinesq‐Burger System," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:9288157
    DOI: 10.1155/2022/9288157
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    References listed on IDEAS

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    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    2. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    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.
    4. Isaiah Elvis Mhlanga & Chaudry Masood Khalique, 2012. "Exact Solutions of Generalized Boussinesq-Burgers Equations and (2+1)-Dimensional Davey-Stewartson Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-8, December.
    5. Isaiah Elvis Mhlanga & Chaudry Masood Khalique, 2012. "Exact Solutions of Generalized Boussinesq‐Burgers Equations and (2+1)‐Dimensional Davey‐Stewartson Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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