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The Fractal Structure Of Analytical Solutions To Fractional Riccati Equation

Author

Listed:
  • ZENONAS NAVICKAS

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania)

  • TADAS TELKSNYS

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania)

  • INGA TELKSNIENE

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania)

  • ROMAS MARCINKEVICIUS

    (��Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania)

  • MINVYDAS RAGULSKIS

    (Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania)

Abstract

Analytical solutions to the fractional Riccati equation are considered in this paper. Solutions to fractional differential equations are expressed in the form of fractional power series in the Caputo algebra. It is demonstrated that solutions to higher-order Riccati fractional equations inherit some solutions from lower-order Riccati equations under special initial conditions. Such nested and fractal-like structure of solutions is investigated by means of analytical fractional differentiation operator techniques and computational experiments.

Suggested Citation

  • Zenonas Navickas & Tadas Telksnys & Inga Telksniene & Romas Marcinkevicius & Minvydas Ragulskis, 2024. "The Fractal Structure Of Analytical Solutions To Fractional Riccati Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-9.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x23401308
    DOI: 10.1142/S0218348X23401308
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