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[en] 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.