Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation*
Zhang Ran-Ran, Xu Wei†, Yang Gui-Dong, Han Qun
       
Stationary PDFs obtained analytically and numerically in the case of α = 0.6, ω 0 = 2.5, k = 1.2, γ = 1.0, D = 0.06, β 1 = 0.05, and β 2 = −0.05: (a) PDF of amplitude A ; (b) PDF of displacement X ; (c) PDF of velocity Y = Ẋ . Here the lines denote the analytical results and the dots refer to the Monte Carlo results.