Boundary Value Problems for a Pseudoparabolic Equation with the Caputo Fractional Derivative

Abstract

We study boundary value problems for a third-order pseudoparabolic equation with variable coefficients and with the Caputo fractional derivative. A priori estimates are derived in the differential and difference settings. These estimates imply the uniqueness of the solution of these problems and its stability with respect to the initial data and right-hand side as well as the convergence of solutions of the associated difference problem to the solution of the differential problem at the rate O(h² + τ), where h and τ are the steps in the space and time variables.