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Stochastic solution to a time-fractional attenuated wave equation
Mark M Meerschaert1, Peter Straka, Yuzhen Zhou
1Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, mcubed@stt.msu.edu.
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.
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