Acta Mechanica

, Volume 230, Issue 6, pp 2137–2144 | Cite as

Fractional thermoelasticity problem for an infinite solid with a cylindrical hole under harmonic heat flux boundary condition

  • Yuriy PovstenkoEmail author
Open Access
Original Paper


The time-fractional heat conduction equation with the Caputo derivative results from the law of conservation of energy and time-nonlocal generalization of the Fourier law with the “long-tail” power kernel. In this paper, we consider an infinite solid with a cylindrical cavity under harmonic heat flux boundary condition. The Laplace transform with respect to time and the Weber transform with respect to the spatial coordinate are used. The solutions are obtained in terms of integrals with integrands being the Mittag-Leffler functions. The numerical results are illustrated graphically.



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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceJan Dlugosz University in CzestochowaCzestochowaPoland

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