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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.], 2017, Volume 21, Number 1, Pages 112–121 (Mi vsgtu1499)  

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

Differential Equations and Mathematical Physics

On nonlocal problem with fractional Riemann–Liouville derivatives for a mixed-type equation

A. V. Tarasenko*, I. P. Egorova

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: The unique solvability is investigated for the problem of equation with partial fractional derivative of Riemann–Liouville and boundary condition that contains the generalized operator of fractional integro-differentiation. The uniqueness theorem for the solution of the problem is proved on the basis of the principle of optimality for a nonlocal parabolic equation and the principle of extremum for the operators of fractional differentiation in the sense of Riemann–Liouville. The proof of the existence of solutions is equivalent to the problem of solvability of differential equations of fractional order. The solution is obtained in explicit form.

Keywords: boundary value problem, generalized fractional integro-differentiation operator, Gauss hypergeometric function, fractional differential equation
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1499

Full text: PDF file (629 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.956.6
MSC: 35M12
Received: June 30, 2016
Revised: October 8, 2016
Accepted: December 9, 2016
First online: April 16, 2017

Citation: A. V. Tarasenko, I. P. Egorova, “On nonlocal problem with fractional Riemann–Liouville derivatives for a mixed-type equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 112–121

Citation in format AMSBIB
\Bibitem{TarEgo17}
\by A.~V.~Tarasenko, I.~P.~Egorova
\paper On nonlocal problem with fractional Riemann--Liouville derivatives
for a~mixed-type equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 1
\pages 112--121
\mathnet{http://mi.mathnet.ru/vsgtu1499}
\crossref{https://doi.org/10.14498/vsgtu1499}
\elib{https://elibrary.ru/item.asp?id=29245100}


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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, “Zadachi so smescheniem dlya nagruzhennogo uravneniya giperbolo-parabolicheskogo tipa s operatorom drobnoi diffuzii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 82–90  mathnet  crossref  elib
    2. 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
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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