Abstract:
The paper is concerned with initial-boundary value problems for a Sobolev-type equation with a Gerasimov–Caputo fractional derivative with memory effect. A priori estimates of the solutions are obtained in the differential and difference forms, which imply their uniqueness and stability with respect to the initial data and the right-hand side, as well as the convergence of the solution of the difference problem to the solution of the differential problem.
Key words:boundary value problems, a priori estimate, Sobolev-type equation, fractional-order differential equation, Gerasimov–Caputo fractional derivative, equations with memory.
References