Fractional Brownian dynamics in proteins.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

Quasielastic neutron scattering and relaxation processes in proteins: analytical and simulation-based models.

The present article gives an overview of analytical and simulation approaches to describe the relaxation dynamics of proteins. Particularly emphasised are recent developments of theoretical models, such as fractional Brownian dynamics. The latter connects dynamical events seen on the pico- to nanosecond time scale, accessible to quasielastic neutron scattering, and functional dynamics of protei...

From NMR relaxation to fractional Brownian dynamics in proteins: results from a virtual experiment.

In a recent simulation study [J. Chem. Phys. 2010, 133, 145101], it has been shown that the time correlation functions probed by nuclear magnetic resonance (NMR) relaxation spectroscopy of proteins are well described by a fractional Brownian dynamics model, which accounts for the wide spectrum of relaxation rates characterizing their internal dynamics. Here, we perform numerical experiments to ...