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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 2, Pages 185–202 (Mi zvmmf10827)  

Numerical analysis of initial-boundary value problem for a Sobolev-type equation with a fractional-order time derivative

M. KH. Beshtokov

Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center, Russian Academy of Sciences, Nalchik, Kabardino-Balkarian Republic, 360004 Russia

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.

DOI: https://doi.org/10.1134/S0044466919020054


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:2, 175–192

Bibliographic databases:

UDC: 519.63
Received: 13.01.2018
Revised: 18.08.2018

Citation: M. KH. Beshtokov, “Numerical analysis of initial-boundary value problem for a Sobolev-type equation with a fractional-order time derivative”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 185–202; Comput. Math. Math. Phys., 59:2 (2019), 175–192

Citation in format AMSBIB
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