FRACTIONAL WAVE EQUATIONS WITH ATTENUATION

Fract Calc Appl Anal. 2013 Mar 1;16(1):262-272. doi: 10.2478/s13540-013-0016-9.

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].

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