Abstract. To describe the dynamics of the relaxation process of convective diffusion under conditions of planned filtration, the authors propose a mathematical model based on the fractional derivative equation with respect to time. The boundary value problem corresponding to this model is formulated, a parallel computing algorithm based on the locally one-dimensional scheme is designed, and the results of numerical implementation of the solution are presented.

Keywords: nonclassical mathematical models, relaxation convection–diffusion process, fractional diffusion equation, boundary-value problems, approximate solutions, parallel algorithms.