Abstract <p>The interporosity fluid flow between the matrix pores and fractures is a major cause of strong wave dispersion and attenuation in the seismic frequency range. A modified interporosity flow equation using fractional derivative is introduced for wave propagation in fluid-saturated double-porosity media. The effects of the interporosity flow on wave dispersion and attenuation are investigated. The reflection and transmission behaviors of elastic waves at the loosely bonded interface between an elastic solid and a fluid-saturated double-porosity solid are investigated. The bonding parameter describing the degrees of bonding between the two media is used in the boundary conditions. The energy ratios are derived by satisfying the interfacial conditions of tractions and displacements. Based on the numerical results, the influences of the interporosity flow and degrees of bonding at the interface on reflection and transmission behaviors are mainly studied. It is observed that the energy ratios are affected noticeably by the interporosity flow and loosely bonded interface.</p>