Entropy 2013, 15(10), 4122-4133; doi:10.3390/e15104122
Article

Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion

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Received: 27 August 2013; in revised form: 22 September 2013 / Accepted: 22 September 2013 / Published: 27 September 2013
(This article belongs to the Special Issue Dynamical Systems)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0< r < R)  and a matrix (R <  r < ∞)  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 < a ≤ 2 and 0 < β ≤ 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.
Keywords: fractional calculus; non-Fourier heat conduction; fractional diffusion-wave equation; perfect thermal contact; Laplace transform; Mittag-Leffler function; Wright function; Mainardi function
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MDPI and ACS Style

Povstenko, Y. Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion. Entropy 2013, 15, 4122-4133.

AMA Style

Povstenko Y. Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion. Entropy. 2013; 15(10):4122-4133.

Chicago/Turabian Style

Povstenko, Yuriy. 2013. "Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion." Entropy 15, no. 10: 4122-4133.


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