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A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods

Author

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  • Mohamed Elbadri

    (Department of Mathematics, Faculty of Sciences and Arts, Jouf University, Tubarjal 74713, Saudi Arabia
    Department of Mathematic, University of Gezira, Wad Madani 21111, Sudan)

  • Mohamed A. Abdoon

    (Department of Basic Sciences (Mathematics), Deanship of Preparatory Year, Shaqra University, Riyadh 15342, Saudi Arabia
    Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym 999129, Sudan)

  • Mohammed Berir

    (Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym 999129, Sudan
    Department of Mathematics, Faculty of Science and Arts, Al-Baha University, Baljurashi 1988, Saudi Arabia)

  • Dalal Khalid Almutairi

    (Department of Mathematics, College of Education (Majmaah), Majmaah University, Al-Majmaah 11952, Saudi Arabia)

Abstract

This study focuses on the solution of the rotationally symmetric Rossler attractor by using the adaptive predictor–corrector algorithm (Apc-ABM-method) and the fractional Laplace decomposition method ( ρ -Laplace DM). Furthermore, a comparison between the proposed methods and Runge–Kutta Fourth Order (RK4) is made. It is discovered that the proposed methods are effective and yield solutions that are identical to the approximate solutions produced by the other methods. Therefore, we can generalize the approach to other systems and obtain more accurate results. In addition to this, it has been shown to be useful for correctly discovering examples via the demonstration of attractor chaos. In the future, the two methods can be used to find the numerical solution to a variety of models that can be used in science and engineering applications.

Suggested Citation

  • Mohamed Elbadri & Mohamed A. Abdoon & Mohammed Berir & Dalal Khalid Almutairi, 2023. "A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods," Mathematics, MDPI, vol. 11(13), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2997-:d:1187261
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    References listed on IDEAS

    as
    1. Mohamed A. Abdoon & Faeza Lafta Hasan & Nidal E. Taha & Devendra Kumar, 2022. "Computational Technique to Study Analytical Solutions to the Fractional Modified KDV-Zakharov-Kuznetsov Equation," Abstract and Applied Analysis, Hindawi, vol. 2022, pages 1-9, June.
    2. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Mohamed Elbadri & Shams A. Ahmed & Yahya T. Abdalla & Walid Hdidi, 2020. "A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-9, September.
    4. Mohamed Elbadri & Zengtao Chen, 2022. "Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-7, June.
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