Stationary response of nonlinear system with Caputo-type fractional derivative damping under Gaussian white noise excitation

Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise

“…The stochastic averaging method which is a versatile and powerful approximate approach has been used by lots of authors. Specifically, Huang and Jin [19] utilized the stochastic averaging method to get the stochastic response and stability of a SDOF stochastic system with fractional derivative damping driven by Gaussian white noise; Chen and Zhu studied the stationary responses [20], stochastic jump and bifurcation [21], stochastic stability [22] and first passage failure [23,24] of stochastic oscillators endowed with fractional derivative damping; Hu and Zhu [25,26] examined the stochastic optimal control of quasi-integrable Hamiltonian systems endowed with fractional derivative damping; Xu and Yang [27] studied the stochastic response of stochastic system endowed with Caputo-type fractional derivative damping driven by Gaussian white noise excitation by using the stochastic averaging method. Xu and Zhang [28] discussed the stationary response of Duffing-Rayleigh system with fractional derivative under Gaussian white noise excitation.…”

Stochastic Bifurcations of a Fractional‐Order Vibro‐Impact System Driven by Additive and Multiplicative Gaussian White Noises

“…Stochastic perturbations are ubiquitous in the real world, so it is necessary to study the dynamical behaviors of the fractionalorder stochastic systems. A lot of methods have been put forward to study the fractional-order stochastic systems, such as the stochastic averaging method [14][15][16][17], multiple scales method [18][19][20], Wiener path integral technique [21], and statistical linearization-based technique [22]. Some recent articles on this topic are as follows.…”

Dynamic Analysis of a Plate on the Generalized Foundation with Fractional Damping Subjected to Random Excitation

“…Response of a strong nonlinear oscillator [17], its reliability function [18], and its stochastic/asymptotic stability [19,20] have been studied by Chen et al They could separate fractional derivative into the equivalent quasilinear dissipative force and quasilinear restoring force [21]. Yang et al studied the stationary and stochastic response of nonlinear system with fractional derivative under white Gaussian noise input [22,23]. Failla and Pirrotta presented a numerical method to calculate the response of a system under stochastic excitation based on the discretization of fractional derivative [24].…”