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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, 250100, **an, China

    Ting-Hui Ning & **ao-Yun Jiang

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  1. Ting-Hui Ning
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  2. **ao-Yun Jiang
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Correspondence to **ao-Yun Jiang.

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The project was supported by the National Natural Science Foundation of China (11072134 and 11102102).

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Ning, TH., Jiang, XY. Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation. Acta Mech Sin 27, 994–1000 (2011). https://doi.org/10.1007/s10409-011-0533-x

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  • DOI: https://doi.org/10.1007/s10409-011-0533-x

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