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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
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    References listed on IDEAS

    as
    1. Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    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. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    4. Vasily E. Tarasov, 2021. "General Fractional Vector Calculus," Mathematics, MDPI, vol. 9(21), pages 1-87, November.
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