Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion.

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

Investigation of Brownian Motion of CuO-Water Nanofluid in a Porous Cavity with Internal Heat Generation by Using of LTNE Model

In this paper, the effect of the Brownian term in natural convection of CuO-Water nanofluid inside a partially filled porous cavity, with internal heat generation has been studied. It is assumed that the viscosity and thermal conductivity of nanofluid consists of a static part and a Brownian part of which is a function of temperature and the volume fraction of nanofluid. Because of internal hea...

Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...

Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion

Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequenc...