Abstract. The mathematical modeling of the dynamics of a non-equilibrium diffusion process in geomedia saturated with saline solutions is considered. On the basis of generalized Hilfer’s fractional derivative, a mathematical model is proposed to describe the fractional-differential dynamics of the process under study, and the numerical–analytical solution of the boundary-value problem corresponding to this model is obtained.

Keywords: nonequilibrium diffusion process, saturated geoporous medium, fractional-order equation, Hilfer biordinal fractional derivative, boundary-value problem, numerical solution, analytical solution.