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Analysis of solutions of the 1D fractional Cattaneo heat transfer equation

Siedlecka Urszula, Ciesielski Mariusz

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 4

87--98

In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.

Analytical solution of Cattaneo equation

Lupa M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

127-132

The Cattaneo equation supplemented by adequate boundary and initial conditions is considered. The solution of this equation is found in analytic way. In the final part of the paper the computations basing on the solution presented are shown.