The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1767–1777

Axisymmetric solutions to fractional diffusion-wave equation in a cylinder under Robin boundary condition

Regular Article

DOI: 10.1140/epjst/e2013-01962-4

Cite this article as:
Povstenko, Y. Eur. Phys. J. Spec. Top. (2013) 222: 1767. doi:10.1140/epjst/e2013-01962-4


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.

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceJan Długosz University in CzȩstochowaCzȩstochowaPoland

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