Transient wave propagation in inhomogeneous porous materials: Application of fractional derivatives

Acoustic wave propagation in inhomogeneous porous material is studied in the time domain. Fractional calculus is used to describe the inertial, viscous and thermal interactions between fluid and structure. A generalized hyperbolic fractional equation (generalized Telegraph equation) for transient sound wave propagation in inhomogeneous material is established. A wave-splitting technique is presented formally for the description of the dynamic equation of the reflection scattering operator.