IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i23p4476-d985529.html
   My bibliography  Save this article

Poincaré Map for Discontinuous Fractional Differential Equations

Author

Listed:
  • Ivana Eliašová

    (Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská Dolina, 842 48 Bratislava, Slovakia)

  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská Dolina, 842 48 Bratislava, Slovakia)

Abstract

We work with a perturbed fractional differential equation with discontinuous right-hand sides where a discontinuity function crosses a discontinuity boundary transversally. The corresponding Poincaré map in a neighbourhood of a periodic orbit of an unperturbed equation is found. Then, bifurcations of periodic boundary solutions are analysed together with a concrete example.

Suggested Citation

  • Ivana Eliašová & Michal Fečkan, 2022. "Poincaré Map for Discontinuous Fractional Differential Equations," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4476-:d:985529
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/23/4476/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/23/4476/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vasily E. Tarasov, 2021. "General Fractional Vector Calculus," Mathematics, MDPI, vol. 9(21), pages 1-87, November.
    2. Vasily E. Tarasov, 2020. "Exact Solutions of Bernoulli and Logistic Fractional Differential Equations with Power Law Coefficients," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    3. Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    4. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    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. Vasily E. Tarasov, 2023. "Multi-Kernel General Fractional Calculus of Arbitrary Order," Mathematics, MDPI, vol. 11(7), pages 1-32, April.
    2. Vasily E. Tarasov, 2020. "Exact Solutions of Bernoulli and Logistic Fractional Differential Equations with Power Law Coefficients," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    3. Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
    4. Vasily E. Tarasov, 2021. "Integral Equations of Non-Integer Orders and Discrete Maps with Memory," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    5. Mohammed Al-Refai & Yuri Luchko, 2023. "The General Fractional Integrals and Derivatives on a Finite Interval," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    6. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    7. Dmitrii Tverdyi & Roman Parovik, 2023. "Hybrid GPU–CPU Efficient Implementation of a Parallel Numerical Algorithm for Solving the Cauchy Problem for a Nonlinear Differential Riccati Equation of Fractional Variable Order," Mathematics, MDPI, vol. 11(15), pages 1-21, July.
    8. Jimin Yu & Zeming Zhao & Yabin Shao, 2023. "On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    9. Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Jesús López-Estrada & Fernando Brambila-Paz, 2022. "Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data," Mathematics, MDPI, vol. 10(5), pages 1-18, March.
    10. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    11. Vasily E. Tarasov, 2021. "General Fractional Calculus: Multi-Kernel Approach," Mathematics, MDPI, vol. 9(13), pages 1-14, June.
    12. Vasily E. Tarasov, 2021. "General Fractional Vector Calculus," Mathematics, MDPI, vol. 9(21), pages 1-87, November.
    13. Vasily E. Tarasov, 2021. "General Fractional Dynamics," Mathematics, MDPI, vol. 9(13), pages 1-26, June.
    14. Vasily E. Tarasov, 2023. "General Fractional Noether Theorem and Non-Holonomic Action Principle," Mathematics, MDPI, vol. 11(20), pages 1-35, October.
    15. Vasily E. Tarasov, 2020. "Non-Linear Macroeconomic Models of Growth with Memory," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    16. Vasily E. Tarasov, 2022. "Fractional Dynamics with Depreciation and Obsolescence: Equations with Prabhakar Fractional Derivatives," Mathematics, MDPI, vol. 10(9), pages 1-34, May.
    17. Zain-Aldeen S. A. Rahman & Basil H. Jasim & Yasir I. A. Al-Yasir & Yim-Fun Hu & Raed A. Abd-Alhameed & Bilal Naji Alhasnawi, 2021. "A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications," Mathematics, MDPI, vol. 9(20), pages 1-25, October.
    18. Vasily E. Tarasov, 2022. "General Non-Local Continuum Mechanics: Derivation of Balance Equations," Mathematics, MDPI, vol. 10(9), pages 1-43, April.

    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:10:y:2022:i:23:p:4476-:d:985529. 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.