title: FRACTIONAL WAVE EQUATIONS WITH ATTENUATION.
abstract: Fractional wave equations with attenuation have been proposed by Caputo [5], Szabo [27], 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].
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA.
authors.forename: Peter
authors.initials: P
authors.lastname: Straka
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA.
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.affiliation: Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: McGough
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA.
authors.forename: Yuzhen
authors.initials: Y
authors.lastname: Zhou
keywords: Fractional derivative; attenuation; continuous time random walk; dispersion; stable law; subordination; wave equation