M. Ochmann et S. Makarov, REPRESENTATION OF THE ABSORPTION OF NONLINEAR-WAVES BY FRACTIONAL DERIVATIVES, The Journal of the Acoustical Society of America, 94(6), 1993, pp. 3392-3399
Fractional derivatives of arbitrary order are incorporated into a mode
l nonlinear equation in order to simulate the absorption mechanism in
a finite frequency domain. That makes it possible to take into account
a power dependence of the absorption coefficient on the frequency at
any real degree. The model gives a mathematical description of a large
set of well-known absorption mechanisms. The method is applied to cal
culate weakly nonlinear oscillations in a nonrigid tube. As a result,
the value of the absorption coefficient and its dependence on the freq
uency are found based on experimental data.