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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2011, Issue 4(25), Pages 25–36
DOI: https://doi.org/10.14498/vsgtu1014
(Mi vsgtu1014)
 

This article is cited in 13 scientific papers (total in 13 papers)

Differential Equations

Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order

O. A. Repina, S. K. Kumykovab

a Dept. of Mathematical Statistics and Econometrics, Samara State Economic University, Samara
b Dept. of Function Theory, Kabardino-Balkar State University, Nal'chik (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: The unique solvability of internally boundary value problem for equation of mixed type of third order with multiple characteristics is investigated. The uniqueness theorem is proved with the restrictions on certain features and different orders of fractional integro-differentiation. The existence of solution is equivalent reduced to a Fredholm integral equation of the second kind.
Keywords: boundary value problem, fractional integro-differentiation operators, Gauss hypergeometric function, Fredholm integral equation.
Original article submitted 17/X/2011
revision submitted – 23/XI/2011
Bibliographic databases:
Document Type: Article
UDC: 517.956.6 + 517.968.23
MSC: Primary 35M12; Secondary 26A33, 33C05
Language: Russian
Citation: O. A. Repin, S. K. Kumykova, “Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(25) (2011), 25–36
Citation in format AMSBIB
\Bibitem{RepKum11}
\by O.~A.~Repin, S.~K.~Kumykova
\paper Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 4(25)
\pages 25--36
\mathnet{http://mi.mathnet.ru/vsgtu1014}
\crossref{https://doi.org/10.14498/vsgtu1014}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu1014
  • https://www.mathnet.ru/eng/vsgtu/v125/p25
  • This publication is cited in the following 13 articles:
    1. Zh. A. Balkizov, “Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain”, J. Math. Sci. (N. Y.), 250:5 (2020), 728–739  mathnet  crossref  mathscinet
    2. Zh. A. Balkizov, “Dirichlet boundary value problem for a third order parabolic-hyperbolic equation with degenerating type and order in the hyperbolicity domain”, Ufa Math. J., 9:2 (2017), 25–39  mathnet  crossref  isi  elib
    3. O. A. Repin, “Zadacha s operatorami Saigo dlya vyrozhdayuschegosya vnutri oblasti giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:3 (2017), 473–480  mathnet  crossref  zmath  elib
    4. V. A. Vodakhova, M. R. Yakhutlova, R. G. Tlimakhova, “Nelokalnaya zadacha dlya uravneniya smeshannogo tipa s dvumya perpendikulyarnymi liniyami vyrozhdeniya”, Sovremennye naukoemkie tekhnologii, 2016, no. 2-3, 416–420  elib
    5. O. A. Repin, S. K. Kumykova, “Boundary-value problem with Saigo operators for mixed type equation of the third order with multiple characteristics”, Russian Math. (Iz. VUZ), 59:7 (2015), 44–51  mathnet  crossref
    6. O. A. Repin, S. K. Kumykova, “On a nonlocal problem for a third-order equation of mixed type with multiple characteristics”, Differential Equations, 51:6 (2015), 767–775  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya modelnogo uravneniya parabolo-giperbolicheskogo tipa tretego poryadka”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 17:4 (2015), 9–20  elib
    8. O. A. Repin, S. K. Kumykova, “Zadacha so smescheniem dlya vyrozhdayuschegosya vnutri oblasti giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(34) (2014), 37–47  mathnet  crossref  zmath  elib
    9. Zh. A. Balkizov, “Analog zadachi Trikomi dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s operatorom Gellerstedta v oblasti giperbolichnosti”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 16:2 (2014), 20–27  elib
    10. Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s operatorom gellerstedta v oblasti giperbolichnosti”, Uravneniya smeshannogo tipa, rodstvennye problemy analiza i informatiki, Tretii Mezhdunarodnyi Rossiisko-Kazakhskii simpozium, Nalchik, 2014, 47–49  elib
    11. Kh. G. Bzhikhatlov, A. G. Ezaova, “Zadacha s nelokalnymi kraevymi usloviyami dlya uravneniya tretego poryadka”, Izvestiya Kabardino-Balkarskogo gosudarstvennogo universiteta, 3:3 (2013), 26–30  elib
    12. I. G. Mamedov, “Trekhmernaya integro-mnogotochechnaya kraevaya zadacha dlya nagruzhennykh volterro-giperbolicheskikh integro-differentsialnykh uravnenii tipa Bianki”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 8–20  mathnet  crossref
    13. O. A. Repin, S. K. Kumykova, “Zadacha so smescheniem dlya uravneniya tretego poryadka s razryvnymi koeffitsientami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(29) (2012), 17–25  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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