Authors: Atanacković, Teodor
Pilipović, Stevan
Zorica, Dušan 
Title: Time distributed-order diffusion-wave equation. Ii. Applications of laplace and fourier transformations
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume: 465
Issue: 2106
First page: 1893
Last page: 1917
Issue Date: 8-Jun-2009
Rank: M21
ISSN: 1364-5021
DOI: 10.1098/rspa.2008.0446
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'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 diffusionwave and fractional telegraph equations are obtained as special cases. Numerical experiments are also performed. An analogue of the maximum principle is also presented.
Keywords: Diffusion-wave equation | Distributed-order fractional derivative | Distributional diffusion-wave equation | Fractional derivative
Publisher: The Royal Society
Project: Serbian Ministry of Sciences, Grants 144019A and 144016

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