ON THE CONVERGENCE OF LOCALLY ONE-DIMENSIONAL SCHEMES FOR THE DIFFERENTIAL EQUATION IN PARTIAL DERIVATIVES OF FRACTIONAL ORDERS IN A MULTIDIMENSIONAL DOMAIN

In this paper, we construct local one-dimensional schemes (LOS) for partial differential equations in partial derivatives of fractional orders in time and space in a multidimensional domain. The validity of the maximum principle for the solution of the differential problem is established. On the basis of the maximum principle, an a priori estimate in the uniform metric is obtained, from which follows the stability and convergence of the difference schemes.