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Time-fractional heat conduction in an infinite medium with a spherical hole under robin boundary condition

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Abstract

The time-fractional heat conduction equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in an infinite medium with a spherical hole in the central symmetric case under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative at the boundary and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary. The integral transforms techniques are used. Several particular cases of the obtained solutions are analyzed. The numerical results are illustrated graphically.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Jan Długosz University in Czcestochowa, al. Armii Krajowej 13/15, 42-200, Czcestochowa, Poland

    Yuriy Povstenko

  2. Department of Computer Science, European University of Informatics and Economics (EWSIE), ul. Białostocka 22, 03-741, Warsaw, Poland

    Yuriy Povstenko

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  1. Yuriy Povstenko
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Correspondence to Yuriy Povstenko.

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Dedicated to the 70th anniversary of Professor Francesco Mainardi

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Povstenko, Y. Time-fractional heat conduction in an infinite medium with a spherical hole under robin boundary condition. fcaa 16, 354–369 (2013). https://doi.org/10.2478/s13540-013-0022-y

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  • DOI: https://doi.org/10.2478/s13540-013-0022-y

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