IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v158y2022ics0960077922001667.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922001667
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111956?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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).
    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).
    Full references (including those not matched with items on IDEAS)

    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. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Abro, Kashif Ali & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2019. "Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 40-45.
    3. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    4. Singh, Harendra, 2021. "Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Li, Zhongfei & Liu, Zhuang & Khan, Muhammad Altaf, 2020. "Fractional investigation of bank data with fractal-fractional Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    7. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Djaoue, Seraphin & Guilsou Kolaye, Gabriel & Abboubakar, Hamadjam & Abba Ari, Ado Adamou & Damakoa, Irepran, 2020. "Mathematical modeling, analysis and numerical simulation of the COVID-19 transmission with mitigation of control strategies used in Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. Xuan, Liu & Ahmad, Shabir & Ullah, Aman & Saifullah, Sayed & Akgül, Ali & Qu, Haidong, 2022. "Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    10. Yusuf, Abdullahi & Qureshi, Sania & Feroz Shah, Syed, 2020. "Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    11. Wang, Wanting & Khan, Muhammad Altaf & Fatmawati, & Kumam, P. & Thounthong, P., 2019. "A comparison study of bank data in fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 369-384.
    12. 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).
    13. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.
    14. Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    15. Ullah, Malik Zaka & Mallawi, Fouad & Baleanu, Dumitru & Alshomrani, Ali Saleh, 2020. "A new fractional study on the chaotic vibration and state-feedback control of a nonlinear suspension system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Berhe, Hailay Weldegiorgis & Qureshi, Sania & Shaikh, Asif Ali, 2020. "Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    17. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    18. 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.
    19. Yusuf, Abdullahi & Tasiu Mustapha, Umar & Abdulkadir Sulaiman, Tukur & Hincal, Evren & Bayram, Mustafa, 2021. "Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    20. Shahram Rezapour & Chernet Tuge Deressa & Azhar Hussain & Sina Etemad & Reny George & Bashir Ahmad, 2022. "A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique," Mathematics, MDPI, vol. 10(4), pages 1-26, February.

    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:eee:chsofr:v:158:y:2022:i:c:s0960077922001667. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.