共查询到20条相似文献,搜索用时 15 毫秒
1.
We obtain martingale characterizations for the generalized space fractional Poisson process (GSFPP) and for counting processes with Bern?tein intertimes. These serve as extensions of the Watanabe's characterization for the classical homogenous Poisson process. The corresponding assertion for the space fractional Poisson process (SFPP) is obtained as a particular case of our results. 相似文献
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We study global and local stabilities of the stationary zero solution to certain infinite-dimensional stochastic differential equations. The stabilities are in terms of fractional powers of the linear part of the drift. The abstract results are applied to semilinear stochastic partial differential equations with non-Lipschitzian drift terms and, in particular, to some specific models of population dynamics. We also expose the stabilizing effect of noise on the otherwise unstable zero solution As a basic tool we use the Forward Inequality, a generalization of Kolmogorov's forward equation; it is an application of Lyapunov's second method with a sequence of Lyapunov functionals 相似文献
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Time-space fractional stochastic Ginzburg-Landau equation driven by Gaussian white noise 总被引:1,自引:0,他引:1
The current article is devoted to the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein-Ulenbeck equations. The dependence of the order of time-fractional derivative, the order of the space-fractional derivative, and the regularity of the initial data are revealed. The global existence and uniqueness of the mild solutions for time-space fractional complex Ginzburg-Landau equation driven by Gaussian white noise are established. 相似文献
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Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out. 相似文献
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We deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Lévy process. For this estimator, we obtain consistency and the asymptotic distribution. Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Lévy process, they can be regarded both as a Lévy generalization of fractional Brownian motion and a fractional generaliza- tion of Lévy process. 相似文献
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建立了有限分形介质中具有吸附效应的分数阶反应扩散积分方程.利用Lap lace变换、广义有限H ankel变换及其相应的逆变换得到了以M ittag-Leffler函数为主要形式的解析解,并研究了解的渐近性态. 相似文献
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In this paper we focus on the Wright hypergeometric matrix functions and incomplete Wright Gauss hypergeometric matrix functions by using Pochhammer matrix symbol. We first introduce the Wright hypergeometric functions of a matrix argument and examine the convergence of these matrix functions in the unit circle, then we discuss the integral representations and differential formulas of the Wright hypergeometric matrix functions. We have also carried out a similar study process for incomplete Wright Gauss hypergeometric matrix functions. Finally, we obtain some results on the transform and fractional calculus of these Wright hypergeometric matrix functions. 相似文献
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Meirav Amram Miriam Dagan Michael Ioshpe Pavel Satianov 《International Journal of Mathematical Education in Science & Technology》2016,47(7):1087-1102
The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages – they have some basic uses in various programming tasks. In this paper, we view the staircase and fractional part functions as a classical example of non-continuous real functions. We introduce some of their basic properties, present some interesting constructions concerning them, and explore some intriguing interpretations of such functions. Throughout the paper, we use these functions in order to explain basic concepts in a first calculus course, such as domain of definition, discontinuity, and oddness of functions. We also explain in detail how, after researching the properties of such functions, one can draw their graph; this is a crucial part in the process of understanding their nature. In the paper, we present some subjects that the first-year student in the exact sciences may not encounter. We try to clarify those subjects and show that such ideas are important in the understanding of non-continuous functions, as a part of studying analysis in general. 相似文献
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Amir Hosein Hadian Rasanan Nastaran Bajalan Kourosh Parand Jamal Amani Rad 《Mathematical Methods in the Applied Sciences》2020,43(3):1437-1466
By the rapid growth of available data, providing data-driven solutions for nonlinear (fractional) dynamical systems becomes more important than before. In this paper, a new fractional neural network model that uses fractional order of Jacobi functions as its activation functions for one of the hidden layers is proposed to approximate the solution of fractional differential equations and fractional partial differential equations arising from mathematical modeling of cognitive-decision-making processes and several other scientific subjects. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer. The linear and nonlinear fractional dynamics are considered as test examples showing the effectiveness and applicability of the proposed neural network. The numerical results are compared with the obtained results of some other networks and numerical approaches such as meshless methods. Numerical experiments are presented confirming that the proposed model is accurate, fast, and feasible. 相似文献
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Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion 总被引:1,自引:0,他引:1
The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively
in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this
process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the
solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution;
the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional
motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition
for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second
order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile
at a given point, and the time history can be described by the fractional calculus. 相似文献
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Won Sang Chung Soroush Zare Hassan Hassanabadi Elham Maghsoodi 《Mathematical Methods in the Applied Sciences》2020,43(11):6950-6967
In this paper, the deformation of the ordinary quantum mechanics is formulated based on the idea of conformable fractional calculus. Some properties of fractional calculus and fractional elementary functions are investigated. The fractional wave equation in 1 + 1 dimension and fractional version of the Lorentz transformation are discussed. Finally, the fractional quantum mechanics is formulated; infinite potential well problem, density of states for the ideal gas, and quantum harmonic oscillator problem are discussed. 相似文献
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Pseudoprocesses, constructed by means of the solutions of higher-order heat-type equations, have been developed by several authors and many related functionals have been analysed by applying the Feynman–Kac functional or by means of the Spitzer identity. We here examine pseudoprocesses wrapped up on circles and derive their explicit signed density measures. By composing the circular pseudoprocesses with positively skewed stable processes, we arrive at genuine circular processes whose distribution is obtained in the form of Poisson kernels. The distribution of circular even-order pseudoprocesses is similar to the Von Mises (or Fisher) circular normal law and to the wrapped up law of Brownian motion. Time-fractional and space-fractional equations related to processes and pseudoprocesses on the unit radius circumference are introduced and analysed. 相似文献
16.
Gutti Jogesh Babu Kesar Singh Yaning Yang 《Annals of the Institute of Statistical Mathematics》2003,55(1):83-94
One-term Edgeworth Expansions for the studentized version of compound Poisson processes are developed. For a suitably defined
bootstrap in this context, the so called one-term Edgeworth correction by bootstrap is also established. The results are applicable
for constructing second-order correct confidence intervals (which make correction for skewness) for the parameter “mean reward
per unit time”.
Research work of Gutti Jogesh Babu was supported in part by NSF grants DMS-9626189 and DMS-0101360. 相似文献
17.
Yongshun Liang Weiyi Su 《分析论及其应用》2007,23(4):354-362
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship. 相似文献
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一个分形函数的分数阶微积分函数 总被引:2,自引:0,他引:2
Based on the combination of fractional calculus with fractal functions, a new type of is introduced; the definition, graph, property and dimension of this function are discussed. 相似文献
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Bernstein modal basis: Application to the spectral Petrov‐Galerkin method for fractional partial differential equations 下载免费PDF全文
In the spectral Petrov‐Galerkin methods, the trial and test functions are required to satisfy particular boundary conditions. By a suitable linear combination of orthogonal polynomials, a basis, that is called the modal basis, is obtained. In this paper, we extend this idea to the nonorthogonal dual Bernstein polynomials. A compact general formula is derived for the modal basis functions based on dual Bernstein polynomials. Then, we present a Bernstein‐spectral Petrov‐Galerkin method for a class of time fractional partial differential equations with Caputo derivative. It is shown that the method leads to banded sparse linear systems for problems with constant coefficients. Some numerical examples are provided to show the efficiency and the spectral accuracy of the method. 相似文献
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The asymptotical behavior of the distributions of stochastic processes defined by multiplicative functions in the set of shifted primes is considered. The first author was supported by Konferenz der deutschen Akademien der Wissenschaften. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Paderborn University, Warburger 100, 33098 Paderborn, Germany. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 441–460, October–December, 1999. 相似文献