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On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations

Author

Listed:
  • Mawia Osman

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Yonghui Xia

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Omer Abdalrhman Omer

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Ahmed Hamoud

    (Department of Mathematics, Taiz University, Taiz P.O. Box 6803, Yemen)

Abstract

In this article, we present the fuzzy Adomian decomposition method (ADM) and fuzzy modified Laplace decomposition method (MLDM) to obtain the solutions of fuzzy fractional Navier–Stokes equations in a tube under fuzzy fractional derivatives. We have looked at the turbulent flow of a viscous fluid in a tube, where the velocity field is a function of only one spatial coordinate, in addition to time being one of the dependent variables. Furthermore, we investigate the fuzzy Elzaki transform, and the fuzzy Elzaki decomposition method (EDM) applied to solving fuzzy linear-nonlinear Schrodinger differential equations. The proposed method worked perfectly without any need for linearization or discretization. Finally, we compared the fuzzy reduced differential transform method (RDTM) and fuzzy homotopy perturbation method (HPM) to solving fuzzy heat-like and wave-like equations with variable coefficients. The RDTM and HPM solutions are simpler than other already existing methods. Several examples are provided to illustrate the methods that have been offered. The results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. These studies are important in the context of the development of the theory of fuzzy partial differential equations.

Suggested Citation

  • Mawia Osman & Yonghui Xia & Omer Abdalrhman Omer & Ahmed Hamoud, 2022. "On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations," Mathematics, MDPI, vol. 10(13), pages 1-49, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2295-:d:852842
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    References listed on IDEAS

    as
    1. Yu, Jianping & Jing, Jian & Sun, Yongli & Wu, Suping, 2016. "(n+1)-Dimensional reduced differential transform method for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 697-705.
    2. Zhu, Yonggui & Chang, Qianshun & Wu, Shengchang, 2005. "Exact solitary-wave solutions with compact support for the modified KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 365-369.
    3. Ali Fareed Jameel & Sarmad A. Jameel Altaie & Sardar Gul Amen Aljabbari & Abbas AlZubaidi & Noraziah Haji Man, 2020. "Double Parametric Fuzzy Numbers Approximate Scheme for Solving One-Dimensional Fuzzy Heat-Like and Wave-Like Equations," Mathematics, MDPI, vol. 8(10), pages 1-26, October.
    4. M. Oberguggenberger & S. Pittschmann, 1999. "Differential Equations With Fuzzy Parameters," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 5(3), pages 181-202, September.
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