Fractional wave equations with attenuation-Reference-Cited by-同舟云学术

Fractional wave equations with attenuation

Published:2012-12-27 Issue:1 Volume:16 Page:262-272
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Straka Peter¹,Meerschaert Mark²,McGough Robert³,Zhou Yuzhen²

Affiliation:

1. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

2. Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA

3. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, 48824, USA

Abstract

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].

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

http://link.springer.com/content/pdf/10.2478/s13540-013-0016-9.pdf

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