Abstract. For geofiltration mathematical model with Atangana–Baleanu fractional derivative, closed solutions of boundary-value problems of filtration theory in homogeneous and layered arrays of finite size are obtained. Problems with nonlocal boundary conditions and the inverse problem of fractional differential filtration dynamics are formulated and solved.

Keywords: mathematical modeling, fractional-differential dynamics of filtration processes, geoporous media, non-classical models, equation of filtration with ABC-fractional derivative, boundary-value problems, closed form solutions.