Abstract : The equivalent fluid model (EFM) describes the acoustic behaviour of rigid porous media with an effective density and compressibility. These physical quantities are complex-valued frequency-dependent functions that can be irrational, cf the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model. The system of equations derived from the EFM can thus involve fractional derivatives in the time domain. In this talk, an investigation of the JCAPL-EFM based on oscillatory-diffusive representations is carried out in order to build a stable and tractable approximated model for numerical simulations in the time domain.