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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 3, Pages 62–69 (Mi ivm9339)  

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

On solvability of nonlocal problem for loaded parabolic-hyperbolic equation

A. V. Tarasenko

Samara State Architecture and Civil Engineering University, 194 Molodogvardeiskaya str., Samara, 443001 Russia

Abstract: We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

Keywords: boundary-value problem, equation of mixed type, operators of fractional integro-differentiation in the Riemann–Liouville sense, generalized operators of fractional integro-differentiation in the M. Saigo sense, Fredholm integral equation of the second kind.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:3, 53–59

Bibliographic databases:

UDC: 517.956
Received: 11.01.2017

Citation: A. V. Tarasenko, “On solvability of nonlocal problem for loaded parabolic-hyperbolic equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 3, 62–69; Russian Math. (Iz. VUZ), 62:3 (2018), 53–59

Citation in format AMSBIB
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\by A.~V.~Tarasenko
\paper On solvability of nonlocal problem for loaded parabolic-hyperbolic equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 3
\pages 62--69
\mathnet{http://mi.mathnet.ru/ivm9339}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 3
\pages 53--59
\crossref{https://doi.org/10.3103/S1066369X18030076}
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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. K. U. Khubiev, “Kraevaya zadacha dlya nagruzhennogo giperbolo-parabolicheskogo uravneniya s vyrozhdeniem poryadka”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast III, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 167, VINITI RAN, M., 2019, 112–116  mathnet  crossref  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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