Spectral analysis of fractional kinetic equations with random data

被引：128

作者：

Anh, VV

Leonenko, NN

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Cardiff Univ, Sch Math, Cardiff CF2 4YH, S Glam, Wales

[3] Kyiv Univ Natl, Dept Math, UA-252601 Kiev, Ukraine

来源：

JOURNAL OF STATISTICAL PHYSICS | 2001年 / 104卷 / 5-6期

基金：

澳大利亚研究理事会;

关键词：

fractional kinetic equation; fractional diffusion equation; scaling laws; renormalised solution; long-range dependence; non-Gaussian scenario; Mittag-Leffler function; Bessel potential; Riesz potential; stable distributions;

D O I：

10.1023/A:1010474332598

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a spectral representation of the mean-square solution of the fractional kinetic equation (also known as fractional diffusion equation) with random initial condition. Gaussian and non-Gaussian limiting distributions of the renormalized solution of the fractional-in-time and in-space kinetic equation are described in terms of multiple stochastic integral representations.

引用

页码：1349 / 1387

页数：39

共 80 条

[51]

Mainardi F., 1995, Nonlinear Waves Solids, V137, P93

[52]

Mainardi F., 1997, FRACTAL FRACT, P291, DOI [DOI 10.1007/978-3-7091-2664-6_7, 10.1007/978-3-662-03425-5, 10.1007/978-3-7091-2664-6_7]

[53]

MAJOR P, 1981, LECT NOTES MATH

[54] FRACTIONAL MODEL EQUATION FOR ANOMALOUS DIFFUSION [J].

METZLER, R ;

GLOCKLE, WG ;

NONNENMACHER, TF .

PHYSICA A, 1994, 211 (01) :13-24

[55]

Miller K. S., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations, DOI DOI 10.1016/S0076-5392(99)80020-4

[56] GENERALIZED BROWNIAN FUNCTIONALS AND THE SOLUTION TO A STOCHASTIC PARTIAL-DIFFERENTIAL EQUATION [J].

NUALART, D ;

ZAKAI, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 1989, 84 (02) :279-296

[57]

OBERHETTINGER F, 1973, FOURIER TRANSFORM DI

[58]

Oldham KB, 1974, Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order

[59]

OSTROVSKII IV, 1995, MATH PHYS ANAL GEOM, V2, P436

[60]

Podulubny I, 1999, Fractional differential equation

← 1 2 3 4 5 6 7 8 →