Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 930297 14 pages doi 2011 930297 Research Article Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates Y. Z. Povstenko1 2 1 Institute of Mathematics and Computer Science Jan Dtugosz University 42200 Czestochowa Poland 2 Department of Computer Science European University of Informatics and Economics EWSIE 03741 Warsaw Poland Correspondence should be addressed to Y. Z. Povstenko 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. 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 p and the exponential Fourier transform with respect to the spatial coordinate z. Numerical results are illustrated graphically. 1. Introduction The time-fractional diffusion-wave equation dau da a u M is a mathematical model of important physical phenomena ranging from amorphous colloid glassy and porous materials through fractals percolation clusters random and disordered media to comb structures dielectrics and semiconductors polymers and biological systems see 1-10 and references therein . The fundamental solution for the fractional diffusion-wave equation in one spacedimension was obtained by Mainardi 11 . Wyss 12 obtained the solutions to the Cauchy problem in terms of H-functions using the Mellin transform. Schneider and Wyss 13 converted the diffusion-wave equation with .
