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Fundamental solutions to time-fractional heat conduction equations in two joint half-lines

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Central European Journal of Physics

Abstract

Heat conduction in two joint half-lines is considered under the condition of perfect contact, i.e. when the temperatures at the contact point and the heat fluxes through the contact point are the same for both regions. The heat conduction in one half-line is described by the equation with the Caputo time-fractional derivative of order α, whereas heat conduction in another half-line is described by the equation with the time derivative of order β. The fundamental solutions to the first and second Cauchy problems as well as to the source problem are obtained using the Laplace transform with respect to time and the cos-Fourier transform with respect to the spatial coordinate. The fundamental solutions are expressed in terms of the Mittag-Leffler function and the Mainardi function.

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Authors and Affiliations

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

    Yuriy Povstenko

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  1. Yuriy Povstenko
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Correspondence to Yuriy Povstenko.

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Povstenko, Y. Fundamental solutions to time-fractional heat conduction equations in two joint half-lines. centr.eur.j.phys. 11, 1284–1294 (2013). https://doi.org/10.2478/s11534-013-0272-7

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  • DOI: https://doi.org/10.2478/s11534-013-0272-7

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