Department of Informatics, University of Oslo, P.O. Box 1080, NO-0316 Oslo, Norway.
J Acoust Soc Am. 2011 Sep;130(3):1125-32. doi: 10.1121/1.3614550.
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
分数导数非常适合描述复杂介质中的波传播。当它们被引入经典波动方程中时，可以对衰减和色散进行建模，从而更好地描述生物组织中的声传播。使用分数导数对固体力学和热传导的传统本构方程进行修正。这些方程用于推导出一个描述衰减和色散规律的非线性波动方程，该方程与观测结果相符。这个波动方程是 Westervelt 方程的推广，也导致了 Khokhlov-Zabolotskaya-Kuznetsov 和 Burgers 方程的分数阶版本。
