NUMERICAL ANALYSIS OF A FRACTIONAL ROTATING PENDULUM OSCILLATOR

This paper proposes a fractional rotating pendulum oscillator based on He’s fractional derivative. The governing fractional equation is obtained by using fractional variational theory and Euler–Lagrange equation. In order to address the nonlinear and fractional operators arising from the considered oscillator, we combine fractional complex transformation with Maclaurin series approximation to convert it into a Duffing-type oscillator. Approximated solutions and frequencies are then obtained by using the spreading residue harmonic balance method. Numerical comparisons with Runge–Kutta method, He’s frequency method and higher-order homotopy perturbation method are presented to verify the proposed technique’s effectiveness. Further analysis of the approximations under different parameters is provided, offering valuable insights for guaranteeing the stability of the rotating oscillation system.