Abstract. The analytical solutions of boundary-value problems with nonlocal boundary conditions are presented for two fractional differential mathematical models of the dynamics of a geomigration process non-equilibrium in time. The models based on the equations with Caputo and Hilfer’s derivatives of fractional order are considered.

Keywords: mathematical modeling, geomigration processes locally nonequilibrium in time, fractional differential mathematical models, systems of fractional differential equations, Caputo and Hilfer derivatives, boundary-value problems, nonlocal boundary conditions.