Stochastic generalized fractional HP equations and applications

Stochastic Fractional HP Equations

In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- tions, for a hyperregular Lagrange function. From the stochastic fractional Hamiltonian equations, Langevin fractional equations were found and numerical simulations were done.

Viability for stochastic differential equations driven by fractional Brownian motion

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is also an alternative global existence result for the fractional differential equations with restrictions on the state.

Generation of random dynamical systems from fractional stochastic delay differential equations

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a Hölder space which is separable.

时间分数阶随机Navier-Stokes方程的存在性与近似可控性结果

Existence and approximate controllability results for time-fractional stochastic Navier-Stokes equations

本文针对时间分数阶随机Navier-Stokes方程，利用不动点技术证明温和解的存在唯一性，并基于分数阶微积分、半群理论等建立近似可控性充分条件。

An averaging principle for fractional stochastic differential equations with Lévy noise

This paper is devoted to the study of an averaging principle for fractional stochastic differential equations in Rnwith Lévy motion, using an integral transform method. We obtain a time-averaged equation under suitable assumptions. Furthermore, we show that the solutions of averaged equation approach the solutions of the original equation. Our results in this paper provide better understanding for effective approximation of fractional dynamical systems with non-Gaussian Lévy noise.

Stochastic integration for fractional Levy process and stochastic differential equation driven by fractional Levy noise

In this paper, based on the white noise analysis of square integrable pure-jump Levy process given by [1], we define the formal derivative of fractional Levy process defined by the square integrable pure-jump Levy process as the fractional Levy noises by considering fractional Levy process as the generalized functional of Levy process, and then we define the Skorohod integral with respect to the fractional Levy process. Moreover, we propose a class of stochastic Volterra equations driven by fractional Levy noises and investigate the existence and uniqueness of their solutions; In addition, we …

具有广义算子的阶数 $1<α<2$ 的随机分数阶发展方程

Stochastic fractional evolution equations of order $1<α<2$ with generalized operators

本文研究具有 Caputo 时间分数阶导数（阶数介于1和2之间）及分数阶空间导数的随机分数阶发展方程的柯西问题，利用广义一致连续解算子在 Colombeau 广义随机过程空间中求得唯一解，并应用于随机分数阶波动方程。

Fractional embeddings and stochastic time

As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said causal. In this case, the fractional embedding becomes coherent.

Stochastic Partial Differential Equations Driven by Fractional Levy Noises

In this paper, we investigate stochastic partial differential equations driven by multi-parameter anisotropic fractional Levy noises, including the stochastic Poisson equation, the linear heat equation, and the quasi-linear heat equation. Well-posedness of these equations under the fractional noises will be addressed. The multi-parameter anisotropic fractional Levy noise is defined as the formal derivative of the anisotropic fractional Levy random field. In doing so, there are two folds involved. First, we consider the anisotropic fractional Levy random field as the generalized functional of t…