Boundary value problems for the generalized modified moisture transfer equation and difference methods for their numerical implementation

Initial boundary value problems with conditions of the first and third kind for a generalized modified moisture transfer equation with a time-fractional derivative are considered. Difference schemes approximating these problems are constructed on a uniform grid. To solve these problems, assuming the existence of a regular solution, a priori estimates in differential and difference forms are obtained. From these estimates follow the uniqueness and continuous dependence of the solution on the input data of the problem, as well as convergence with the speed $O(h^2+\tau^2)$.