In this paper a recently developed technique relying on the globally-evolving-based
generalized density evolution equation (GE-GDEE) is extended. It is applied to determining …

In the present survey, some progress in the stochastic dynamics and fractional optimal
control of quasi integrable Hamiltonian systems with fractional derivative damping is …

This article addresses three classes of fractional oscillators named Class I, II and III. It is
known that the solutions to fractional oscillators of Class I type are represented by the Mittag …

The generalized fractional derivative is a useful tool for describing the mechanical property
of viscoelastic dampers in vehicles. However, the complex integral form of the generalized …

This paper presents a wavelet-based method for determining response evolutionary power
spectrum density (EPSD) of linear/non-linear systems endowed with fractional derivative …

Stochastic response of a plate on the generalized foundation driven by random excitation is
solved in this paper. Governing differential equation is obtained by employing the Galerkin …

A statistical linearization method is proposed for determining the response moment of multi-
degree-of-freedom (MDOF) nonlinear systems, endowed with fractional elements and …

In this paper, we introduce an efficient method for identifying fractional dynamic systems
using extended sparse regression and cross-validation techniques. The former identifies …

The novelty and main contributions of this paper are reflected in four aspects. First, we
introduce multi-fractional phasor in Theorem 1. Second, we propose the motion phasor …

In this paper, stochastic bifurcations of a fractional-order smooth and discontinuous (SD)
oscillator composed of different viscoelastic materials are studied. As a widely applicable …