Initial-boundary problems for the moisture transfer equation with fractional derivatives of different orders and a non-local linear source

The work is devoted to initial-boundary value problems for the fractional order moisture transfer equation with a non-local linear source and variable coefficients. Under the assumption of the existence of a regular solution for each of the considered first and third boundary value problems, an a priori estimate in differential form is obtained, which implies the uniqueness and continuous dependence of the solution on the input data of the original problem. With each differential problem associate a difference scheme on a uniform grid. Assuming the existence of a solution for each difference problem, an a priori estimate in a difference form is obtained, which implies the uniqueness and stability of the solution to the difference problem with respect to the right-hand side and initial data. Due to the linearity of the initial-boundary value problems under consideration, the obtained estimates in difference form allow us to state the convergence of the solution of each difference problem to the solution of the original differential problem (assuming the existence of the latter in the class of sufficiently smooth functions) at a rate equal to the order of the approximation error. Numerical calculations are carried out, illustrating the theoretical results obtained in the work.