To Boundary-Value Problems for Degenerating Pseudoparabolic Equations With Gerasimov–Caputo Fractional Derivative

In this paper we consider a boundary-value problems for degenerating pseudoparabolic equation with variable coefficients and with Gerasimov–Caputo fractional derivative. To solve the problem we obtain a priori estimates in differential and difference settings. These a priori estimates imply uniqueness and stability of the solution with respect to the initial data and the right-hand side on the layer, as well as the convergence of the solution of each of the difference problem to the solution of the corresponding differential problem.

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