Free-space Fresnel diffraction for the approximation of fractional Fourier transform

Fractional Fourier transformation of an object can be approximated by the object's free-space Fresnel diffraction pattern under some restricted conditions and plane wave illumination according to Hua's method. A better approximation is achieved under least-squared conditions developed in this paper. Simulation results verify that our theoretical development works for any fractional order a compared with the previous approach.     

树的四类控制参数的束缚数

图的束缚数是图的控制数研究中的一个重要方面，它在某种程度上反映了图的控制数对边数的敏感度．本文通过对图的结构特征的分析．研究了树的四类控制参数的束缚数，即控制数，强控制数，弱控制数．分数控制数的束缚数．分别给出了其紧的上界．     

Statistical Multiplexing of Homogeneous Fractional Brownian Streams

In this paper, the statistical multiplexing of independent fractional Brownian traffic streams with the same Hurst value 0.5<H<1 is studied. The buffer overflow probabilities based on steady-state and transient queue length tail distributions are used respectively as the common performance criterion. Under general conditions, the minimal buffer allocation to the merged traffic is identified in either case so that strictly positive bandwidth savings are realized. Impact of the common H value on multiplexing gains is investigated. The analytical results are applicable in data network engineering problems, where ATM is deployed as the transport network carrying long-range dependent data traffic.     

两参数分数Wiener过程增量的一般形式

§1Introductionandresults A2-parameterGaussianprocess{Z(t,s);t,s≥0}iacalleda2-parameterfractional Wienerprocesswithorderα(0<α<1),ifZ(0,0)=0a.s.EZ(s,t)=0anditscovariance EZ(t1,s1)Z(t2,s2)={|t1|2α+|t2|2α-|t2-t1|2α}{|s1|2α+|s2|2α-|s2-s1|2α}/4.LetR=[x1,x2]×[y1,y2],DT={(x,y)∶0≤x,y≤bT,xy≤T}.Let0相似文献   

IMPLICIT DIFFERENCE APPROXIMATION FOR A TIME FRACTIONAL ADVECTION-DISPERSION EQUATION

In this paper, a time fractional advection-dispersion equation is considered. From the relationship between the Caputo derivative and the Grunwald derivative, the Caputo derivative is approximated by using the Griinwald derivative. An implicit difference approximation for this equation is proposed. We prove that this approximation is unconditionally stable and convergent. Finally, numerical examples are given.     

SOLVABILITY FOR FRACTIONAL-ORDER TWO-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

In this paper, we are concerned with the existence of solution to a boundary value problem of nonlinear fractional differential equation at resonance. By means of the coincidence degree theory, the existence of solution is obtained.     

具有逐项分数阶导数的微分方程边值问题解的存在性

研究了一类具有逐项分数阶导数的微分方程边值问题.对参数的各种取值情况进行了全面的分析,运用Banach压缩映射原理和Schauder不动点定理,得到并证明了边值问题解的存在性定理.最后,给出了两个例子来证明结论有效.     

Analysis of an Implicit Finite Difference Scheme for Time Fractional Diffusion Equation

Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper.     

奇摄动分数阶微分方程的渐近解

本文研究了一类奇摄动非线性分数阶微分方程初值问题.利用伸长变量构造出解的形式展开式,并利用微分不等式理论,证明了解的一致有效的渐近式.所得的结果具有较好精度的近似解.     

Fractional‐order switching type control law design for adaptive sliding mode technique of 3D fractional‐order nonlinear systems

In this article, an adaptive sliding mode technique based on a fractional‐order (FO) switching type control law is designed to guarantee robust stability for a class of uncertain three‐dimensional FO nonlinear systems with external disturbance. A novel FO switching type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criteria of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. Effectiveness of the proposed control scheme is illustrated through numerical simulations. © 2015 Wiley Periodicals, Inc. Complexity 21: 363–373, 2016