Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab

• Autorzy: Kukla S. , Siedlecka U.

Identyfikatory

DOI

10.17512/jamcm.2015.4.10

• Języki publikacji: EN

Abstrakty

EN

In this paper the Laplace transformation for solving the problem of fractional heat conduction in a two-layered slab has been applied. The different orders of Caputo derivative in the time-fractional equation governed the heat transfer in the layers are assumed. The inverse Laplace transform by using a numerical method is determined. The numerical results obtained by using of the eigenfunctions method and by numerically inverting the Laplace transform are compared.

Słowa kluczowe

EN

fractional heat conduction; two-layered slab; Laplace transformation

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 4
• Strony: 105--113
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Kukla S.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Siedlecka U.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

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• [7] Povstenko Y., Fractional heat conduction in infinite one-dimensional composite medium. Journal of Thermal Stresses 2013, 36, 351-363.
• [8] Siedlecka U., Kukla S., A solution to the problem of time-fractional heat conduction in a multilayer slab, Journal of Applied Mathematics and Computational Mechanics 2015, 14(3), 95-102.
• [9] Podlubny I., Fractional Differential Equations, Academic Press, San Diego 1999.
• [10] Valko P.P., Abate J., Numerical inversion of 2-D Laplace transforms applied to fractional diffusion equations, Applied Numerical Mathematics 2005, 53, 73-88.
• [11] Wang Q., Zhan H., On different numerical inverse Laplace methods for solute transport problems, Advances in Water Resources 2015, 75, 80-92.
• [12] Povstenko Y., Klekot J., The Dirichlet problem for time-fractional advection-diffusion equation in a half-space, Journal of Applied Mathematics and Computational Mechanics 2015, 14(2), 73-83.