Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation  被引量:2

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

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作  者:Ting-Hui Ning Xiao-Yun Jiang 

机构地区:[1]School of Mathematics, Shandong University, 250100 Jinan, China

出  处:《Acta Mechanica Sinica》2011年第6期994-1000,共7页力学学报(英文版)

基  金:supported by the National Natural Science Foundation of China(11072134 and 11102102)

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 〈 α≤ 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.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 〈 α≤ 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.

关 键 词:Fractional Fourier law Fractional heat conduction equation - Spherical coordinate system - The separation of variables Mittag-Leffler function 

分 类 号:O29[理学—应用数学] O551.3[理学—数学]

 

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