Initial-Boundary Value Problems for the Moisture Transfer Equation with Different Order Fractional Derivatives and Nonlocal Linear Source

We study the initial-boundary value problemsfor the moisture transfer equation of a fractional order with a nonlocal linear source and variable coefficients.Assuming the existence of a regular solution for each of the first and third boundary value problems under consideration,we obtain an a priori estimate in differential formwhich implies the uniqueness and continuous dependence of the solution on the input data.To each differential problem we associate a difference scheme on a uniform grid.Assuming the existence of a solution for each difference problem,we obtain an a priori estimate in difference formwhich implies the uniqueness of the solution to the difference problem and its stabilityunder the right-hand side and initial data.Owing to the linearity of the initial-boundary value problems under consideration,the estimates obtained in difference form allow us to assert the convergence of the solution of each difference problemto 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.Also, we present the numerical calculations that illustrate the theoretical results.