Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion

被引：28

作者：

Povstenko, Yuriy ^{[1
,2
]}

机构：

[1] Jan Dlugosz Univ Czestochowa, Inst Math & Comp Sci, PL-42200 Czestochowa, Poland

[2] European Univ Informat & Econ EWSIE, Dept Comp Sci, PL-03741 Warsaw, Poland

来源：

ENTROPY | 2013年 / 15卷 / 10期

关键词：

fractional calculus; non-Fourier heat conduction; fractional diffusion-wave equation; perfect thermal contact; Laplace transform; Mittag-Leffler function; Wright function; Mainardi function; ANOMALOUS DIFFUSION; ENTROPY; DYNAMICS; EQUATION; RELAXATION; TRANSPORT; TSALLIS;

D O I：

10.3390/e15104122

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0 < r < R) and a matrix (R < r < infinity) being in perfect thermal contact at r = R is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 0 < alpha <= 2 and 0 < beta < 2, respectively. The Laplace transform with respect to time is used. The approximate solution valid for small values of time is obtained in terms of the Mittag-Leffler, Wright, and Mainardi functions.

引用

页码：4122 / 4133

页数：12

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