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Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion
Institute of Mathematics and Computer Science, Jan Długosz University in Częstochowa, Armii Krajowej 13/15, Częstochowa 42-200, Poland
Department of Computer Science, European University of Informatics and Economics (EWSIE) Białostocka 22, Warsaw 03-741, Poland
Received: 27 August 2013; in revised form: 22 September 2013 / Accepted: 22 September 2013 / Published: 27 September 2013
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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Povstenko, Y. Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion. Entropy 2013, 15, 4122-4133.
Povstenko Y. Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion. Entropy. 2013; 15(10):4122-4133.
Povstenko, Yuriy. 2013. "Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion." Entropy 15, no. 10: 4122-4133.