Cauchy problem for fractional diffusion equations

被引：338

作者：

Eidelman, SD ^{[1
]}

Kochubei, AN ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Math Inst, UA-01601 Kiev, Ukraine

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 199卷 / 02期

关键词：

fractional diffusion equation; fractional derivative; Fox's H-function; fundamental solution; Levi method;

D O I：

10.1016/j.jde.2003.12.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an evolution equation with the regularized fractional derivative of an order alpha epsilon (0, 1) with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables. Such equations describe diffusion on inhomogeneous fractals. A fundamental solution of the Cauchy problem is constructed and investigated. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：211 / 255

页数：45

共 27 条

[1] Spectral analysis of fractional kinetic equations with random data [J].

Anh, VV ;

Leonenko, NN .

JOURNAL OF STATISTICAL PHYSICS, 2001, 104 (5-6) :1349-1387

[2]

[Anonymous], 1992, IDEAS METHODS MATH P

[3]

Baeumer B., 2001, FRACT CALCU APPL ANA, V4, P481

[4]

Bazhlekova E, 2001, THESIS TU EINDHOVEN

[5]

BAZHLEKOVA E, 1998, FRACT CALC APPL ANAL, V1, P255

[6]

Braaksma B.L.J., 1962, Compos. Math, V15, P239

[7]

Dzherbashyan MM, 1968, Izv Akad Nauk Arm SSR, Ser Mat, V3, P3

[8]

Eidelman S.D., 1969, PARABOLIC SYSTEMS, P469

[9]

El-Sayed AM, 1995, J FRACT CALC, V7, P89

[10]

Erdelyi A, 1955, HIGHER TRANSCENDENTA, V3

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