RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Tr.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (305 kB)
References: PDF file   HTML file

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

UDC: 519.63

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}