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

作者：Ning Ting Hui; Jiang Xiao Yun^*

来源：Acta Mechanica Sinica, 2011, 27(6): 994-1000.

DOI：10.1007/s10409-011-0533-x

• Fractional Fourier law
• Fractional heat conduction equation
• Spherical coordinate system
• The separation of variables
• Mittag-Leffler function

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.

• 出版日期2011-12
• 单位山东大学