Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition |
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Authors: | Yuriy Povstenko |
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Institution: | 1. Institute of Mathematics and Computer Science, Jan D?ugosz University in Cz?stochowa, al. Armii Krajowej 13/15, 42-200, Cz?stochowa, Poland 2. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Naukova 3-b, 79060, Lviv, Ukraine
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Abstract: | The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically. |
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