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New Type Modelling of the Circumscribed Self-Excited Spherical Attractor

Author

Listed:
  • Mohammad Partohaghighi

    (Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA)

  • Ali Akgül

    (Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey)

  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

Abstract

The fractal–fractional derivative with the Mittag–Leffler kernel is employed to design the fractional-order model of the new circumscribed self-excited spherical attractor, which is not investigated yet by fractional operators. Moreover, the theorems of Schauder’s fixed point and Banach fixed existence theory are used to guarantee that there are solutions to the model. Approximate solutions to the problem are presented by an effective method. To prove the efficiency of the given technique, different values of fractal and fractional orders as well as initial conditions are selected. Figures of the approximate solutions are provided for each case in different dimensions.

Suggested Citation

  • Mohammad Partohaghighi & Ali Akgül & Rubayyi T. Alqahtani, 2022. "New Type Modelling of the Circumscribed Self-Excited Spherical Attractor," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:732-:d:758670
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    References listed on IDEAS

    as
    1. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    2. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Leutcho, Gervais Dolvis & Jafari, Sajad & Hamarash, Ibrahim Ismael & Kengne, Jacques & Tabekoueng Njitacke, Zeric & Hussain, Iqtadar, 2020. "A new megastable nonlinear oscillator with infinite attractors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

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