IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2997-d1187261.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2997/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/13/2997/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    2. Ariza-Hernandez, Francisco J. & Martin-Alvarez, Luis M. & Arciga-Alejandre, Martin P. & Sanchez-Ortiz, Jorge, 2021. "Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Attia, Nourhane & Akgül, Ali & Seba, Djamila & Nour, Abdelkader, 2020. "An efficient numerical technique for a biological population model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Izadi, Mohammad & Yüzbaşı, Şuayip & Adel, Waleed, 2022. "Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    6. Defterli, Ozlem, 2021. "Comparative analysis of fractional order dengue model with temperature effect via singular and non-singular operators," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. McAllister, A. & McCartney, M. & Glass, D.H., 2023. "Stability, collapse and hyperchaos in a class of tri-trophic predator–prey models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    8. H. Mesgarani & Y. Esmaeelzade Aghdam & A. Beiranvand & J. F. Gómez-Aguilar, 2024. "A Novel Approach to Fuzzy Based Efficiency Assessment of a Financial System," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1609-1626, April.
    9. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Cecilia Berardo & Iulia Martina Bulai & Ezio Venturino, 2021. "Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators," Mathematics, MDPI, vol. 9(20), pages 1-18, October.
    11. Matouk, A.E. & Lahcene, Bachioua, 2023. "Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    12. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    13. Feng, Yi-Ying & Yang, Xiao-Jun & Liu, Jian-Gen & Chen, Zhan-Qing, 2023. "Mechanical investigations of local fractional magnetorheological elastomers model on Cantor sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    14. A. E. Matouk & T. N. Abdelhameed & D. K. Almutairi & M. A. Abdelkawy & M. A. E. Herzallah, 2023. "Existence of Self-Excited and Hidden Attractors in the Modified Autonomous Van Der Pol-Duffing Systems," Mathematics, MDPI, vol. 11(3), pages 1-13, January.
    15. Xie, Jiaquan & Zhao, Fuqiang & He, Dongping & Shi, Wei, 2022. "Bifurcation and resonance of fractional cubic nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2997-:d:1187261. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.