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1.
In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.  相似文献   

2.
The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne et al. (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.  相似文献   

3.
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, α-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.  相似文献   

4.
小数时延补偿算法的设计及应用   总被引:1,自引:0,他引:1  
小数时延补偿是数字信号处理中的一个难点,在VLBI、阵列信号处理和其它应用领域有多种实现方法。比较了几种常用的时延补偿方法:频域补偿法、基于最小均方误差准则滤波法、拉格朗日(Lagrange)插值法和基于Farrow结构的滤波器组的方法,得到的结论是相对于频域补偿法和其他时域补偿的方法,Lagrange插值法具有操作简单、易于实现、适用范围广的优点,而采用Farrow结构对时延变化的控制能力会更强。采用Farrow结构与Lagrange插值相结合能够获得比较理想的插值效果。详细介绍了基于Farrow结构的Lagrange插值滤波器组的设计及在遥测阵信号处理中的应用,并与已有的频域补偿方法作了比较。  相似文献   

5.
In this paper we show that a change in the signs of some of the metric components of the solution of the field equations for the classical cosmic string results in a solution which we interpret as a time-dependent wall composed of tachyons. We show that the walls have the property of focusing the paths of particles which pass through them. As an illustration of this focusing, we demonstrate the results of a simple simulation of the interaction between one such tachyon wall and a rotating disk of point masses. This interaction leads to the temporary formation of spiral structures. These spiral structures exist for a time on the order of one galactic rotation. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

6.
This paper presents an analytic solution of the equations of motion of an artificial satellite, obtained using non singular elements for eccentricity. The satellite is under the influence of the gravity field of a central body, expanded in spherical harmonics up to an arbitrary degree and order. We discuss in details the solution we give for the components of the eccentricity vector. For each element, we have divided the Lagrange equations into two parts: the first part is integrated exactly, and the second part is integrated with a perturbation method. The complete solution is the sum of the so-called “main” solution and of the so-called “complementary” solution. To test the accuracy of our method, we compare it to numerical integration and to the method developed in Kaula (Theory of Satellite Geodesy, Blaisdell publ. Co., New York. 1966), expressed in classical orbital elements. For eccentricities which are not very small, the two analytical methods are almost equivalent. For low eccentricities, our method is much more accurate.  相似文献   

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