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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.], 2016, Volume 20, Number 1, Pages 43–53 (Mi vsgtu1461)  

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

Differential Equations and Mathematical Physics

An internal boundary value problem with the Riemann–Liouville operator for the mixed type equation of the third order

O. A. Repinab, S. K. Kumykovac

a Samara State Technical University, Samara, 443100, Russian Federation
b Samara State University of Economics, Samara, 443090, Russian Federation
c Kabardino-Balkar State University, Nalchik, 360004, Russia

Abstract: The unique solvability of the internal boundary value problem is investigated for the mixed type equation of the third order with Riemann–Liouville operators in boundary condition. The uniqueness theorem is proved for the different orders of operators of fractional integro-differentiation when the inequality constraints on the known functions exist. The existence of solution is verified by the method of reduction to Fredholm equations of the second kind, which unconditional solvability follows from the uniqueness of the solution of the problem.

Keywords: mixed type equation, Fredholm equation, Cauchy problem, fractional operators in the sense of Riemann–Liouville integro-differentiation

DOI: https://doi.org/10.14498/vsgtu1461

Full text: PDF file (665 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.956.6
MSC: 35M12
Original article submitted 21/XI/2015
revision submitted – 13/II/2016

Citation: O. A. Repin, S. K. Kumykova, “An internal boundary value problem with the Riemann–Liouville operator for the mixed type equation of the third order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:1 (2016), 43–53

Citation in format AMSBIB
\Bibitem{RepKum16}
\by O.~A.~Repin, S.~K.~Kumykova
\paper An internal boundary value problem with~the Riemann--Liouville operator for the mixed type equation of the third order
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 1
\pages 43--53
\mathnet{http://mi.mathnet.ru/vsgtu1461}
\crossref{https://doi.org/10.14498/vsgtu1461}
\zmath{https://zbmath.org/?q=an:06964471}
\elib{http://elibrary.ru/item.asp?id=26898082}


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    This publication is cited in the following articles:
    1. A. G. Ezaova, “Odnoznachnaya razreshimost odnoi zadachi tipa zadachi Bitsadze–Samarskogo dlya uravneniya s razryvnymi koeffitsientami”, Vladikavk. matem. zhurn., 20:4 (2018), 50–58  mathnet  crossref
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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