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Mat. Tr., 2018, Volume 21, Number 2, Pages 72–101 (Mi mt339)  

Nonlocal Boundary Value Problems for Sobolev-Type Fractional Equations and Grid Methods for Solving Them

M. KH. Beshtokov

Kabardino-Balkar State University, Nal'chik

Abstract: 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.

Key words: nonlocal boundary value problem, a priori estimate, Sobolev-type equation, fractional-order differential equation, Gerasimov-Caputo fractional derivative.

DOI: https://doi.org/10.17377/mattrudy.2018.21.203

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English version:
Siberian Advances in Mathematics, 2019, 29:1, 1–21

UDC: 519.63
Received: 17.01.2018

Citation: M. KH. Beshtokov, “Nonlocal Boundary Value Problems for Sobolev-Type Fractional Equations and Grid Methods for Solving Them”, Mat. Tr., 21:2 (2018), 72–101; Siberian Adv. Math., 29:1 (2019), 1–21

Citation in format AMSBIB
\Bibitem{Bes18}
\by M.~KH.~Beshtokov
\paper Nonlocal Boundary Value Problems for Sobolev-Type Fractional Equations and Grid Methods for Solving Them
\jour Mat. Tr.
\yr 2018
\vol 21
\issue 2
\pages 72--101
\mathnet{http://mi.mathnet.ru/mt339}
\crossref{https://doi.org/10.17377/mattrudy.2018.21.203}
\transl
\jour Siberian Adv. Math.
\yr 2019
\vol 29
\issue 1
\pages 1--21
\crossref{https://doi.org/10.3103/S1055134419010012}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064912461}


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