Numerical analysis of a fractional nonlinear oscillator with coordinate-dependent mass

In this paper, we propose a combined technique for solving the fractional modification of the nonlinear oscillator with coordinate-dependent mass. It is an efficient method based on the fractional complex transform and the global residue harmonic balance method (called as FCT-GRHBM). The approximations and frequencies of this fractional nonlinear oscillator are given without linearization. Numerical comparisons with Runge–Kutta method are provided to confirm the efficiency of FCT-GRHBM. The sensitive analysis of the log errors and the frequencies with respect to different parameters is also investigated in detail.