Time-fractional diffusion equation with time dependent diffusion coefficient

被引：30

作者：

Fa, KS ^{[1
]}

Lenzi, EK ^{[1
]}

机构：

[1] Univ Estadual Maringa, Dept Fis, BR-87020900 Maringa, Parana, Brazil

来源：

PHYSICAL REVIEW E | 2005年 / 72卷 / 01期

关键词：

D O I：

10.1103/PhysRevE.72.011107

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We consider the time-fractional diffusion equation with time dependent diffusion coefficient given by (0O(C)tW)-W-alpha(x,t)=D(alpha,gamma)t(gamma)[partial derivative W-2(x,t)/partial derivative x(2)], where O-0((C)t)alpha is the Caputo operator. We investigate its solutions in the infinite and the finite domains. The mean squared displacement and the mean first passage time are also considered. In particular, for alpha=0, the mean squared displacement is given by < x(2)>similar to t(gamma) and we verify that the mean first passage time is finite for superdiffusive regimes.

引用

页数：4

共 25 条

[1] 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

[2] CTRW pathways to the fractional diffusion equation [J].

Barkai, E .

CHEMICAL PHYSICS, 2002, 284 (1-2) :13-27

[3] DIFFUSION IN A FIELD OF HOMOGENEOUS TURBULENCE .2. THE RELATIVE MOTION OF PARTICLES [J].

BATCHELOR, GK .

PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1952, 48 (02) :345-362

[4]

Carpinteri A, 2014, Fractals and Fractional Calculus in Continuum Mechanics, DOI [10.1007/978-3-7091-2664-6, DOI 10.1007/978-3-7091-2664-6]

[5] Anomalous diffusion, solutions, and first passage time: Influence of diffusion coefficient [J].

Fa, KS ;

Lenzi, EK .

PHYSICAL REVIEW E, 2005, 71 (01)

[6] Power law diffusion coefficient and anomalous diffusion: Analysis of solutions and first passage time [J].

Fa, KS ;

Lenzi, EK .

PHYSICAL REVIEW E, 2003, 67 (06) :7

[7]

Gardiner C. W, 1997, HDB STOCHASTIC METHO

[8] Mean first passage time for anomalous diffusion [J].

Gitterman, M .

PHYSICAL REVIEW E, 2000, 62 (05) :6065-6070

[9] FOX FUNCTION REPRESENTATION OF NON-DEBYE RELAXATION PROCESSES [J].

GLOCKLE, WG ;

NONNENMACHER, TF .

JOURNAL OF STATISTICAL PHYSICS, 1993, 71 (3-4) :741-757

[10] Fractional diffusion modeling of ion channel gating -: art. no. 051915 [J].

Goychuk, I ;

Hänggi, P .

PHYSICAL REVIEW E, 2004, 70 (05) :9

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