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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 4(37), Pages 22–32 (Mi vsgtu1348)  

This article is cited in 2 scientific papers (total in 2 papers)

Differential Equations

On a class of nonlocal problems for hyperbolic equations with degeneration of type and order

O. A. Repinab, S. K. Kumykovac

a Samara State Technical University
b Samara State University of Economics
c Kabardino-Balkar State University, Nal'chik

Abstract: Nonlocal problems for the second order hyperbolic model equation were studied in the characteristic area. The type and order of equations degenerate on the same line $ y = 0 $. Nonlocal condition is given by means of fractional integro-differentiation of arbitrary order on the boundary. Nonlocal condition connects fractional derivatives and integrals of the desired solution. For different values of order operators of fractional integro-differentiation within the boundary condition the unique solvability of the considered problems was proved or non-uniqueness of the solution was estimated.

Keywords: nonlocal boundary value problem, fractional integro-differentiation operators, Cauchy problem, second kind Volterra integral equation, Abel integral equation

DOI: https://doi.org/10.14498/vsgtu1348

Full text: PDF file (733 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.956.326
MSC: 35M12
Original article submitted 23/X/2014
revision submitted – 05/XI/2014

Citation: O. A. Repin, S. K. Kumykova, “On a class of nonlocal problems for hyperbolic equations with degeneration of type and order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(37) (2014), 22–32

Citation in format AMSBIB
\Bibitem{RepKum14}
\by O.~A.~Repin, S.~K.~Kumykova
\paper On a class of nonlocal problems for hyperbolic equations with degeneration of type and order
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 4(37)
\pages 22--32
\mathnet{http://mi.mathnet.ru/vsgtu1348}
\crossref{https://doi.org/10.14498/vsgtu1348}
\zmath{https://zbmath.org/?q=an:06968930}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Dolgopolov, I. N. Rodionova, V. M. Dolgopolov, “Ob odnoi nelokalnoi zadache dlya uravneniya Eilera–Darbu”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:2 (2016), 259–275  mathnet  crossref  zmath  elib
    2. A. V. Tarasenko, “On solvability of nonlocal problem for loaded parabolic-hyperbolic equation”, Russian Math. (Iz. VUZ), 62:3 (2018), 53–59  mathnet  crossref  isi
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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