THE FRACTAL STRUCTURE OF ANALYTICAL SOLUTIONS TO FRACTIONAL RICCATI EQUATION

Zenonas Navickas, Tadas Telksnys, Inga Telksniene, Romas Marcinkevicius and Minvydas Ragulskis
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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

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-9

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.

Keywords: Fractional Differential Equation; Operator Calculus; Analytical Solution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401308

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