Space-time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

被引：9

作者：

Shi, Long ^{[1
,2
]}

Yu, Zuguo ^{[1
]}

Mao, Zhi ^{[1
]}

Xiao, Aiguo ^{[1
]}

Huang, Hailan ^{[1
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] Cent South Univ Forest & Technol, Inst Math & Phys, Changsha 410004, Hunan, Peoples R China

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2013年 / 392卷 / 23期

关键词：

Space-time fractional diffusion equation; Caputo fractional derivative; Riesz fractional derivative; Coupled continuous time random walk; Asymptotic behavior; FOKKER-PLANCK EQUATIONS; ANOMALOUS DIFFUSION; WAVE-EQUATIONS; DYNAMICS; FINANCE; TRANSPORT;

D O I：

10.1016/j.physa.2013.08.021

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier-Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：5801 / 5807

页数：7

共 37 条

[1]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[2] ANOMALOUS DIFFUSION IN ONE DIMENSION [J].

BALAKRISHNAN, V .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1985, 132 (2-3) :569-580

[3] From continuous time random walks to the fractional Fokker-Planck equation [J].

Barkai, E ;

Metzler, R ;

Klafter, J .

PHYSICAL REVIEW E, 2000, 61 (01) :132-138

[4] ANOMALOUS DIFFUSION IN DISORDERED MEDIA - STATISTICAL MECHANISMS, MODELS AND PHYSICAL APPLICATIONS [J].

BOUCHAUD, JP ;

GEORGES, A .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1990, 195 (4-5) :127-293

[5] Stochastic foundations of fractional dynamics [J].

Compte, A .

PHYSICAL REVIEW E, 1996, 53 (04) :4191-4193

[6] Transport behavior of coupled continuous-time random walks [J].

Dentz, Marco ;

Scher, Harvey ;

Holder, Devora ;

Berkowitz, Brian .

PHYSICAL REVIEW E, 2008, 78 (04)

[7]

Feller W., 1966, An introduction to probability theory and its applications, V2

[8] LANGEVIN-EQUATIONS FOR CONTINUOUS-TIME LEVY FLIGHTS [J].

FOGEDBY, HC .

PHYSICAL REVIEW E, 1994, 50 (02) :1657-1660

[9] Discrete and continuous random walk models for space-time fractional diffusion [J].

Gorenflo, R ;

Vivoli, A ;

Mainardi, F .

NONLINEAR DYNAMICS, 2004, 38 (1-4) :101-116

[10] Continuous-time random walk and parametric subordination in fractional diffusion [J].

Gorenflo, Rudolf ;

Mainardi, Francesco ;

Vivoli, Alessandro .

CHAOS SOLITONS & FRACTALS, 2007, 34 (01) :87-103

← 1 2 3 4 →