Equation of motion of a point oscillator containing fractional friction

M. V. Yashina^a, M. T. Aleroev^a, T. S. Aleroev^b, A. N. Lebedev^a, A. F. Smyk<sup>a

a</sup> Moscow State Automobile and Road Technical University
^b Moscow State University of Civil Engineering

Abstract: In this paper, we examine the motion of a point oscillator under the influence of fractional friction. The behavior of the eigenfrequencies is studied and the graphs of the corresponding eigenfunctions are plotted.

Keywords: fractional calculus, oscillator, Begley–Torvik equation, eigenvalue, eigenfunction

UDC: 517.9+531.32

MSC: 34A08, 26A33, 74H45

DOI: 10.36535/2782-4438-2025-246-65-71