On the convergence of a high order approximation difference scheme for the modified equation of fractional order moisture transfer

The first boundary value problem for the modified moisture transfer equation with two Gerasimov-Caputo fractional differentiation operators of different orders $\alpha, \beta$ is studied. A difference scheme of a higher order of accuracy is constructed on a uniform grid. A priori estimates for different values of $\alpha, \beta$ are obtained by the method of energy inequalities for solving the difference problem. The obtained estimates imply the uniqueness and stability of the solution with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem at a rate equal to the order of approximation.