Fractional dynamics in the Rayleigh’s piston

•Dynamical analysis of the Rayleigh piston.•Power law approximation in the Fourier domain.•Application of fractional calculus and fractional Brownian motion in the Rayleigh piston dynamical analysis.

This paper studies the dynamics of the Rayleigh piston using the modeling tools of Fractional Calculus. Several numerical experiments examine the effect of distinct values of the parameters. The time responses are transformed into the Fourier domain and approximated by means of power law approximations. The description reveals characteristics usual in Fractional Brownian phenomena.