Response of a non-linear system with restoring forces governed by fractional derivatives—Time domain simulation and statistical linearization solution

Fractional rheological models for thermomechanical systems. Dissipation and free energies

“…Therefore, the fractional and Volterra models provide view points which are not reconcilable. It is appropriate to observe that, for solid viscoelastic materials, some experimental observations are particularly in agreement with models using fractional derivatives, because of the power law behavior of the stress relaxation function for viscoelastic materials as given by (1.1) (see [7] [19,36] [ 26,34,31]). The creep function for such models also has power law form.…”

“…The creep function for such models also has power law form. Such experimental backing has motivated many studies of materials with fading memory given by a fractional derivative, including [6,22,4,14,17,30,23] and in the frequency domain [19,36]. Many experimental observations on a variety of materials subject to a constant load show plastic behavior, which can be described by the fractional derivative approach.…”

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

“…Spanous et al presented a standard formulation for modeling vibration of systems with frequency-dependent parameters and fractional properties [11]. They developed a linearizationbased solution to a stochastic nonlinear fractional equation to analyze nonlinear random vibration of a beam with fractional properties [12,13]. Wahi and Chatterjee studied effect of the delay and fractional derivative terms in oscillations of a resonator [14].…”

First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation

“…However, the application of fractional derivative in stochastic dynamical system occurred very late, only very few references can be found [8][9][10].…”