Stochastic solution to a time-fractional attenuated wave equation.
نویسندگان
چکیده
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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ورودعنوان ژورنال:
- Nonlinear dynamics
دوره 70 2 شماره
صفحات -
تاریخ انتشار 2012