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Fractional Calculus and Applied Analysis

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Volume 16, Issue 1

Issues

Fractional wave equations with attenuation

Peter Straka / Mark Meerschaert / Robert McGough / Yuzhen Zhou
Published Online: 2012-12-27 | DOI: https://doi.org/10.2478/s13540-013-0016-9

Abstract

Fractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

MSC: Primary 35J05, 26A33; Secondary 60E07

Keywords: fractional derivative; wave equation; stable law; continuous time random walk; subordination; attenuation; dispersion

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About the article

Published Online: 2012-12-27

Published in Print: 2013-03-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 16, Issue 1, Pages 262–272, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0016-9.

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© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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