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Open AccessArticle

Time-Fractional Heat Conduction in Two Joint Half-Planes

1
Institute of Mathematics and Computer Science, Faculty of Mathematical and Natural Sciences, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland
2
Institute of Mathematics, Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Armii Krajowej 21, 42-200 Czestochowa, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(6), 800; https://doi.org/10.3390/sym11060800
Received: 4 June 2019 / Revised: 13 June 2019 / Accepted: 14 June 2019 / Published: 16 June 2019
(This article belongs to the Special Issue Symmetry in Complex Systems)
The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver–Stehfest method. We give a graphical representation of the numerical results. View Full-Text
Keywords: fractional calculus; non-Fourier heat conduction; Caputo derivative; Fourier transform; Laplace transform fractional calculus; non-Fourier heat conduction; Caputo derivative; Fourier transform; Laplace transform
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MDPI and ACS Style

Povstenko, Y.; Klekot, J. Time-Fractional Heat Conduction in Two Joint Half-Planes. Symmetry 2019, 11, 800. https://doi.org/10.3390/sym11060800

AMA Style

Povstenko Y, Klekot J. Time-Fractional Heat Conduction in Two Joint Half-Planes. Symmetry. 2019; 11(6):800. https://doi.org/10.3390/sym11060800

Chicago/Turabian Style

Povstenko, Yuriy; Klekot, Joanna. 2019. "Time-Fractional Heat Conduction in Two Joint Half-Planes" Symmetry 11, no. 6: 800. https://doi.org/10.3390/sym11060800

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