Axisymmetric solutions to fractional diffusion-wave equation in a cylinder under Robin boundary condition
Institute of Mathematics and Computer Science, Jan Długosz University in Czȩstochowa, al. Armii Krajowej 13/15, 42-200 Czȩstochowa, Poland
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Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
The axisymmetric time-fractional diffusion-wave equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in a cylinder under the prescribed linear combination of the values of the sought function and the values of its normal derivative at the boundary. The fundamental solutions to the Cauchy, source, and boundary problems are investigated. The Laplace transform with respect to time and finite Hankel transform with respect to the radial coordinate are used. The solutions are obtained in terms of Mittag-Leffler functions. The numerical results are illustrated graphically.
© EDP Sciences, Springer-Verlag, 2013