Advances in Difference Equations
Volume 2011 (2011), Article ID 930297, 14 pages
doi:10.1155/2011/930297
Research Article

Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates

Y. Z. Povstenko1,2

1Institute of Mathematics and Computer Science, Jan Długosz University, 42200 Częstochowa, Poland
2Department of Computer Science, European University of Informatics and Economics (EWSIE), 03741 Warsaw, Poland

Received 8 December 2010; Accepted 6 February 2011

Academic Editor: J. J. Trujillo

Copyright © 2011 Y. Z. Povstenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time 𝑡 , the Hankel transform with respect to the radial coordinate 𝑟 , the finite Fourier transform with respect to the angular coordinate 𝜑 , and the exponential Fourier transform with respect to the spatial coordinate 𝑧 . Numerical results are illustrated graphically.