Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

被引：12
|
作者：
Ning, Ting-Hui [1 ]
Jiang, Xiao-Yun [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
来源：
ACTA MECHANICA SINICA | 2011年 / 27卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Fractional Fourier law; Fractional heat conduction equation; Spherical coordinate system; The separation of variables; Mittag-Leffler function; DIFFUSION-WAVE EQUATION; MULTIDIMENSIONAL SOLUTIONS; ANOMALOUS TRANSPORT; CAUCHY-PROBLEM; RANDOM-WALK; STRESSES; DYNAMICS;
D O I：
10.1007/s10409-011-0533-x
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, using the fractional Fourier law, we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system. The method of variable separation is used to solve the timefractional heat conduction equation. The Caputo fractional derivative of the order 0 < alpha a parts per thousand currency sign 1 is used. The solution is presented in terms of the Mittag-Leffler functions. Numerical results are illustrated graphically for various values of fractional derivative.
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页码：994 / 1000
页数：7
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