@article {Atanackovic1893,
author = {Atanackovic, Teodor M. and Pilipovic, Stevan and Zorica, Dusan},
title = {Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations},
volume = {465},
number = {2106},
pages = {1893--1917},
year = {2009},
doi = {10.1098/rspa.2008.0446},
publisher = {The Royal Society},
abstract = {A Cauchy problem for a time distributed-order multi-dimensional diffusion-wave equation containing a forcing term is reinterpreted in the space of tempered distributions, and a distributional diffusion-wave equation is obtained. The distributional equation is solved in the general case of weight function (or distribution). Solutions are given in terms of solution kernels (Green{\textquoteright}s functions), which are studied separately for two cases. The first case is when the order of the fractional derivative is in the interval [0, 1], while, in the second case, the order of the fractional derivative is in the interval [0, 2]. Solutions of fractional diffusion-wave and fractional telegraph equations are obtained as special cases. Numerical experiments are also performed. An analogue of the maximum principle is also presented.},
issn = {1364-5021},
URL = {http://rspa.royalsocietypublishing.org/content/465/2106/1893},
eprint = {http://rspa.royalsocietypublishing.org/content/465/2106/1893.full.pdf},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}