Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab. (English) Zbl 07251920
Summary: 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.
References:
| [1] | Haji-Sheikh, A.; Beck, J. V., Temperature solution in multi-dimensional multi-layer bodies, International Journal of Heat and Mass Transfer, 45, 1865-1877 (2002) · Zbl 0992.80014 |
| [2] | Özişik, M. N., Heat Conduction, Wiley, New York (1993) |
| [3] | Povstenko, Y., Linear Fractional Diffusion-wave Equation for Scientists and Engineers, Birkhauser, New York (2015) · Zbl 1331.35004 |
| [4] | Povstenko, Y., Fractional heat conduction in a semi-infinite composite body, Communications in Applied and Industrial Mathematics, 6, 1, e-482 (2014) · Zbl 1329.35337 |
| [5] | Povstenko, Y., Fundamental solutions to time-fractional heat conduction equations in two joint half-lines, Central European Journal of Physics, 11, 1184-1294 (2013) |
| [6] | Povstenko, Y., Fractional heat conduction in an infinite medium with a spherical inclusion, Entropy, 15, 4122-4133 (2013) · Zbl 1339.80007 |
| [7] | Povstenko, Y., Fractional heat conduction in infinite one-dimensional composite medium, Journal of Thermal Stresses, 36, 351-363 (2013) |
| [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, 14, 3, 95-102 (2015) · Zbl 1515.74019 |
| [9] | Podlubny, I., Fractional Differential Equations, Academic Press, San Diego (1999) · Zbl 0918.34010 |
| [10] | Valko, P. P.; Abate, J., Numerical inversion of 2-D Laplace transforms applied to fractional diffusion equations, Applied Numerical Mathematics, 53, 73-88 (2005) · Zbl 1060.65681 |
| [11] | Wang, Q.; Zhan, H., On different numerical inverse Laplace methods for solute transport problems, Advances in Water Resources, 75, 80-92 (2015) |
| [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, 14, 2, 73-83 (2015) · Zbl 07251888 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
