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Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading

1
Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland
2
Department of Law, Administration and Management, Jan Dlugosz University in Czestochowa, Zbierskiego 2/4, 42-200 Czestochowa, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(5), 689; https://doi.org/10.3390/sym11050689 (registering DOI)
Received: 22 April 2019 / Revised: 12 May 2019 / Accepted: 15 May 2019 / Published: 18 May 2019
(This article belongs to the Special Issue Symmetry in Complex Systems)
PDF [346 KB, uploaded 18 May 2019]

Abstract

The time-fractional heat conduction equation follows from the law of conservation of energy and the corresponding time-nonlocal extension of the Fourier law with the “long-tail” power kernel. The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with two external half-infinite slits with the prescribed heat flux across their surfaces. The integral transform technique is used. The solution is obtained in the form of integrals with integrand being the Mittag–Leffler function. A graphical representation of numerical results is given.
Keywords: fractional calculus; Caputo derivative; generalized Fourier law; Laplace transform; Fourier transform; Mittag–Leffler function fractional calculus; Caputo derivative; generalized Fourier law; Laplace transform; Fourier transform; Mittag–Leffler function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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MDPI and ACS Style

Povstenko, Y.; Kyrylych, T. Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading. Symmetry 2019, 11, 689.

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