A fractional order theory of poroelasticity

•A time memory formalism in the flux-pressure constitutive relation, ruling fluids diffusion phenomenon occurring in several classes of porous media is studied.•The memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo’s fractional derivative.•The resulting flux-pressure law is applied to the classic confined compression test problem of a sand sample. In such a case, the classical Darcy equation may lead to inaccurate estimates of the settlement time.•It is shown that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo’s fractional derivative.