分数因子和分数哈密顿图

本文介绍了图的分数方面,将图中基于整数的定义和变量转化为分数形式．介绍了分数图论的一些新结果,特别是关于分数因子和分数哈密顿图的新结果,其中包括了作者最近得到的一些关于分数(g,f)-因子的若干结果．进而,提出了还没有解决的几个新问题．     

Fractional Sobolev-type inequalities

Here we present univariate Sobolev-type fractional inequalities involving fractional derivatives of Canavati, Riemann–Liouville and Caputo types. The results are general L _p inequalities forward and converse on a closed interval. We give an application to a fractional ODE. We present also the mean Sobolev-type fractional inequalities.     

The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises

The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order α > 1 driven by a fractional noise. We prove the existence and uniqueness of the global mild solution for the considered equation by the fixed point principle. The solutions for SPDEs with fractional noises can be approximated by the solution for the averaged stochastic systems in the sense of p-moment under some suitable assumptions.     

分数阶微分方程的比较定理

本文给出了非线性Riemann—Liouville分数阶微分方程和Caputo分数阶微分方程与相应的非线性Volterra积分方程的等价性,并在此基础上建立了分数阶微分方程的比较定理．     

Generalized Fractional Trace Variational Identity and A New Fractional Integrable Couplings of Soliton Hierarchy

Based on fractional isospectral problems and general bilinear forms, the generalized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.     

一类含高阶Riemann-Liouville型分数阶导数脉冲微分方程的通解

本文首先运用迭代法获得一类含多项Riemann-Liouville型分数阶导数的微分方程的连续通解,然后应用数学归纳法得到这类脉冲微分方程的分片连续通解. 所得结果归结于脉冲分数阶微分方程领域,对分数阶微分方程研究者有参考意义.     

Fractional Integrals on Product Manifolds

In this paper, the authors give a mixed norm estimate for the multi-parameter fractional integrals on product measurable spaces. This estimate is applied to obtain the boundedness for the fractional integrals of Nagel-Stein type on product manifolds, the fractional integral of Folland-Stein type with rough convolution kernels on product homogeneous groups, and the discrete fractional integrals of Stein-Wainger type. The research was supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025).     

一类推广的离散分数阶Gronwall不等式

离散不等式,特别是离散的Gronwall不等式已被广泛应用于差分方程的研究.近年来,分数阶微分方程引起很多学者的关注.因此,利用一种新的分数阶和分的定义和不等式的方法,讨论一类更一般的离散分数阶Gronwall不等式.     

分数阶微分方程的一些新结果

第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质．第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性．第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性．第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性．第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性（次线性）条件下C310,11正解存在的充分必要条件．最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性．     

非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性

本文研究一类非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性,利用一些标准的不动点定理进行证明.     

Fractional differential and integral operations via cumulative approach

In this study, a fractal operator model of cumulative processes is described. Accordingly, differential and integral operators of the fractional calculus are derived by the fractal operator model of a cumulative process. In order to exhibit the relation between our cumulative approach and fractional calculus, vertical motion of a body is handled within these frameworks. Thereby, regard to our assessments, the underlying physical mechanism of the success of the fractional differintegral operators in describing stochastic complex systems is uncovered to some extent.     

Fractional Bilinear Stochastic Equations with the Drift in the First Fractional Chaos

Abstract

In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise.     

(2,q)阶分数差分方程的解

首次提出了一种分数阶差分,分数阶和分以及分数阶差分方程的定义,并给出(2,q)阶常系数分数阶差分方程的具体解法.     

关于分数可消去图的若干结果

令G=(V(G),E(G))是一个图,并令9和f是两个定义在V(G)上的整数值函数且对所有的x∈V(G)有g(x)≤f(z)成立．若对G的每一条边e都存在G的一个分数(g,f)-因子G_h使得h(e)=0,其中h是G_h的示性函数,则称G是一个分数(g,f)-消去图,若在G中删去E′■E(G),|E′|=k后,所得图有分数完美匹配,则称G是分数k-边-可消去的。本文给出了图是1-可消去,2-可消去和k-边-可消去的与韧度和孤立韧度相关的充分条件。证明了这些结果在一定意义上是最好可能的．     

分数(k,q)阶差分方程的解

本文首次提出了一种分数阶差分,分数阶和分以及分数阶差分方程的定义,并利用Z变换理论,给出(k,q)阶常系数分数阶差分方程的具体解法.     

关于带有三点边值的非线性分数阶积分微分方程的解的存在性和惟一性

本文考虑一个带有三点边值的非线性分数阶积分微分方程,并分别用Krasnoselskii不动点定理和Banach压缩映像原理建立了其解的存在性和惟一性的充分条件.     

分数阶微分方程多点分数阶边值问题

研究分数阶微分方程多点分数阶边值问题解的存在性与唯一性,利用不动点定理,得到了边值问题存在唯一解和至少存在1个解的充分条件.     

On Fractional Brownian Processes

We use Liouville spaces in order to prove the existence of some different fractional -Brownian motion ( 0 < 1 ), or fractional ( , )-Brownian sheets. There are also applications to the Wiener stochastic integral with respect to these -Brownian.     

关于分数因子两个开问题的解答

本文指出极小连通二部分数1-因子不一定是极小2-连通图.研究了σ₂（G）与分数k-因子存在性之间的关系,指出存在一个特例在满足阶数n≥4k-5,δ（G）≥k且σ₂（G）≥n条件下,图G不存在分数k-因子.     

Stability of Neutral Fractional Neural Networks with Delay

This paper studies stability of neutral fractional neural networks with delay. By introducing the definition of norm and using the uniform stability, the su?cient condition for uniform stability of neutral fractional neural networks with delay is obtained.