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New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor

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  • Akgül, Ali
  • Partohaghighi, Mohammad

Abstract

The purpose of this study is to present and examine a novel non-integer model of the circumscribed self-excited spherical strange attractor, which has not been worked yet. To design the fractional-order model, we use the Caputo-Fabrizio derivative. In order to ensure the existence of the solution Picard-Lindel and fixed-point theories are provided. Moreover, the stability of the considered fractional-order model is shown using the Picard iteration and fixed point theory approach. To get the approximate solutions of the proposed fractional model an efficient numerical scheme called the fractional Euler method(FEM) is used. To see the performance of the used method, the behavior of the numerical solutions of the model is examined under various initial conditions(ICs) and fractional orders. Considerable chaotic behaviors of the solutions are obtained which prove the accuracy and reliability of FEM.

Suggested Citation

  • Akgül, Ali & Partohaghighi, Mohammad, 2022. "New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922001667
    DOI: 10.1016/j.chaos.2022.111956
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    References listed on IDEAS

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    1. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    2. Ramesh Ramamoorthy & Sajjad Shaukat Jamal & Iqtadar Hussain & Mahtab Mehrabbeik & Sajad Jafari & Karthikeyan Rajagopal & Shijian Cang, 2021. "A New Circumscribed Self-Excited Spherical Strange Attractor," Complexity, Hindawi, vol. 2021, pages 1-8, June.
    3. Chunmei Wang & Chunhua Hu & Jingwei Han & Shijian Cang, 2016. "A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-6, December.
    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. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    6. 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).
    7. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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