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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2020, Volume 31, Number 2, Pages 18–31
DOI: https://doi.org/10.26117/2079-6641-2020-31-2-18-31
(Mi vkam400)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

The inverse problem for a mixed loaded equation with the riemann-liouville operator in a rectangular domain

U. Sh. Ubaydullayev

National University of Uzbekistan named after Mirzo Ulugbek
Full-text PDF (272 kB) Citations (1)
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Abstract: In this paper, we study the inverse problem for a mixed loaded equation with the Riemann-Liouville and Caputo operator in a rectangular domain. A criterion for the uniqueness and existence of a solution to the inverse problem is established. The solution of the problem is constructed in the form of the sum of a series of eigenfunctions of the corresponding one-dimensional spectral problem. It is proved that the unique solvability of the inverse problem substantially depends on the choice of the boundary of a rectangular region. An example is constructed in which the inverse problem with homogeneous conditions has a nontrivial solution. Estimates are obtained that allow substantiating the convergence of series in the class of regular solutions of this equation and the stability of the solution of the inverse problem from boundary data.
Keywords: loaded equation, Riemann-Liouville operator, inverse problem, uniqueness criterion and existence, small denominators, sustainability.
Document Type: Article
UDC: 517.95+517.956.6
MSC: Primary 35M10; Secondary 35M20
Language: Russian
Citation: U. Sh. Ubaydullayev, “The inverse problem for a mixed loaded equation with the riemann-liouville operator in a rectangular domain”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 31:2 (2020), 18–31
Citation in format AMSBIB
\Bibitem{Uba20}
\by U.~Sh.~Ubaydullayev
\paper The inverse problem for a mixed loaded equation with the riemann-liouville operator in a rectangular domain
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2020
\vol 31
\issue 2
\pages 18--31
\mathnet{http://mi.mathnet.ru/vkam400}
\crossref{https://doi.org/10.26117/2079-6641-2020-31-2-18-31}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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