Nonlocal boundary value problems for~Sobolev-type fractional equations and grid methods for~solving them

M. Kh. Beshtokov

Matematičeskie trudy, Tome 21 (2018) no. 2, pp. 72-101.

Résumé

We consider nonlocal boundary value problems for a Sobolev-type equation with variable coefficients with fractional Gerasimov–Caputo derivative. The main result of the article consists in proving a priori estimates for solutions to nonlocal boundary value problems both in differential and difference form obtained under the assumption of the existence of a solution $u(x,t)$ in a class of sufficiently smooth functions. These inequalities imply the uniqueness and stability of a solution with respect to the initial data and right-hand side and also the convergence of the solution to the difference problem to the solution to the differential problem.

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