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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 12, Pages 59–71 (Mi ivm8759)  
This article is cited in 3 scientific papers (total in 3 papers)

A problem with generalized fractional integro-differentiation operator of an arbitrary order

O. A. Repina, S. K. Kumykovab

a Chair of Mathematical Statistics and Econometrics, Samara State Economic University, Samara, Russia
b Chair of Function Theory and Functional Analysis, Kabardino-Balkarian State University, Nalchik, Russia
Full-text PDF (212 kB) Citations (3)
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Abstract: For a degenerate hyperbolic equation we study a problem with fractional integro-differentiation operators in the boundary condition on the characteristic part of the boundary. We determine intervals of variation of parameters of generalized operators of an arbitrary order with the Gauss hypergeometric function with which the problem is either uniquely solvable or has more than one solution.
Keywords: Riemann–Liouville integral and derivative of a fractional order, Volterra and Abel integral equations, Gauss hypergeometric function, resolvent of the kernel.
Received: 17.10.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 12, Pages 50–60
DOI: https://doi.org/10.3103/S1066369X12120067
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: O. A. Repin, S. K. Kumykova, “A problem with generalized fractional integro-differentiation operator of an arbitrary order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 12, 59–71; Russian Math. (Iz. VUZ), 56:12 (2012), 50–60
Citation in format AMSBIB
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\by O.~A.~Repin, S.~K.~Kumykova
\paper A problem with generalized fractional integro-differentiation operator of an arbitrary order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
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\pages 59--71
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 12
\pages 50--60
\crossref{https://doi.org/10.3103/S1066369X12120067}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872236059}
Linking options:
  • https://www.mathnet.ru/eng/ivm8759
  • https://www.mathnet.ru/eng/ivm/y2012/i12/p59
    • This publication is cited in the following 3 articles:
    1. O. A. Repin, S. K. Kumykova, “Nelokalnaya zadacha dlya vyrozhdayuschegosya giperbolicheskogo uravneniya”, Izv. vuzov. Matem., 2017, no. 7, 50–56  mathnet
    2. O. A. Repin, S. K. Kumykova, “On the solvability of nonlocal problem for a hyperbolic equation of the second kind”, Russian Math. (Iz. VUZ), 60:9 (2016), 46–52  mathnet  crossref  isi
    3. O. A. Repin, S. K. Kumykova, “Ob odnom klasse nelokalnykh zadach dlya giperbolicheskogo uravneniya s vyrozhdeniem tipa i poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(37) (2014), 22–32  mathnet  crossref  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Full-text PDF :122
    References:74
    First page:9
     
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