title: Stochastic solution to a time-fractional attenuated wave equation.
abstract: The power law wave equation uses two different fractional derivative terms to model wave propagation with power law attenuation. This equation averages complex nonlinear dynamics into a convenient, tractable form with an explicit analytical solution. This paper develops a random walk model to explain the appearance and meaning of the fractional derivative terms in that equation, and discusses an application to medical ultrasound. In the process, a new strictly causal solution to this fractional wave equation is developed.
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824,  mcubed@stt.msu.edu.
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.forename: Peter
authors.initials: P
authors.lastname: Straka
authors.forename: Yuzhen
authors.initials: Y
authors.lastname: Zhou
authors.forename: Robert J
authors.initials: RJ
authors.lastname: McGough