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Mat. Tr., 2011, Volume 14, Number 1, Pages 99–125 (Mi mt208)  

This article is cited in 22 scientific papers (total in 22 papers)

On some integro-differential operators in the class of harmonic functions and their applications

V. V. Karachika, B. K. Turmetovb, B. T. Torebekb

a South Ural State University, Chelyabinsk, Russia
b Kh. Yasavi International Kazakh-Turkish University, Turkestan, Kazakhstan

Abstract: We study properties of integro-differential operators generalizing the operators of the Riemann–Liouville and Caputo fractional differentiation in the class of harmonic functions. The properties obtained are applied to examine some local and nonlocal boundary value problems for the Laplace equation in the unit ball.

Key words: Laplace equation, Riemann–Liouville operator, Kaputo operator, nonlocal boundary value problem.

Full text: PDF file (275 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2012, 22:2, 115–134

Bibliographic databases:

UDC: 517.956.225+517.572
Received: 17.02.2010

Citation: V. V. Karachik, B. K. Turmetov, B. T. Torebek, “On some integro-differential operators in the class of harmonic functions and their applications”, Mat. Tr., 14:1 (2011), 99–125; Siberian Adv. Math., 22:2 (2012), 115–134

Citation in format AMSBIB
\Bibitem{KarTurTor11}
\by V.~V.~Karachik, B.~K.~Turmetov, B.~T.~Torebek
\paper On some integro-differential operators in the class of harmonic functions and their applications
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 1
\pages 99--125
\mathnet{http://mi.mathnet.ru/mt208}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858659}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 2
\pages 115--134
\crossref{https://doi.org/10.3103/S1055134412020046}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. T. Torebek, “Ob odnom analoge tretei kraevoi zadachi dlya uravneniya Laplasa s granichnym operatorom drobnogo poryadka v smysle Kaputo”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 13:2 (2011), 62–68  elib
    2. A. S. Berdyshev, B. Kh. Turmetov, B. J. Kadirkulov, “Some properties and applications of the integrodifferential operators of Hadamard–Marchaud type in the class of harmonic functions”, Siberian Math. J., 53:4 (2012), 600–610  mathnet  crossref  mathscinet  isi
    3. B. T. Torebek, B. K. Turmetov, “On solvability of a boundary value problem for the Poisson equation with the boundary operator of a fractional order”, Boundary Value Problems, 2013 (2013)  crossref  mathscinet  zmath  elib  scopus
    4. A. E. Bekaeva, V. V. Karachik, B. Kh. Turmetov, “On solvability of some boundary value problems for polyharmonic equation with Hadamard–Marchaud boundary operator”, Russian Math. (Iz. VUZ), 58:7 (2014), 11–24  mathnet  crossref
    5. A. S. Berdyshev, A. Cabada, B. Kh. Turmetov, “On solvability of a boundary value problem for a nonhomogeneous biharmonic equation with a boundary operator of a fractional order”, Acta Math. Sci., 34:6 (2014), 1695–1706  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. A. Sadybekov, B. Kh. Turmetov, B. T. Torebek, “Solvability of nonlocal boundary-value problems for the Laplace equation in the ball”, Electron. J. Differ. Equ., 2014, 157  mathscinet  zmath  isi
    7. M. A. Muratbekova, K. M. Shinaliyev, B. K. Turmetov, “On solvability of a nonlocal problem for the Laplace equation with the fractional-order boundary operator”, Bound. Value Probl., 2014, 29  crossref  zmath  isi  elib  scopus
    8. B. T. Torebek, “Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications”, Ufa Math. J., 7:3 (2015), 73–83  mathnet  crossref  isi  elib
    9. V. V. Karachik, M. A. Sadybekov, B. T. Torebek, “Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball”, Electron. J. Differ. Equ., 2015, 244  zmath  isi  elib
    10. B. J. Kadirkulov, M. Kirane, “On solvability of a boundary value problem for the Poisson equation with a nonlocal boundary operator”, Acta Math. Sci., 35:5 (2015), 970–980  crossref  zmath  isi  elib  scopus
    11. A. S. Berdyshev, A. Cabada, B. Kh. Turmetov, “On solvability of some boundary value problem for polyharmonic equation with boundary operator of a fractional order”, Appl. Math. Model., 39:15 (2015), 4548–4569  crossref  mathscinet  isi  elib  scopus
    12. B. Kh. Turmetov, “Solvability of fractional analogues of the Neumann problem for a nonhomogeneous biharmonic equation”, Electron. J. Differ. Equ., 2015, 82  mathscinet  zmath  isi  elib
    13. B. Kh. Turmetov, B. T. Torebek, “Modified Bavrin operators and their applications”, Differ. Equ., 51:2 (2015), 243–254  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    14. B. T. Torebek, B. Kh. Turmetov, “On solvability of exterior boundary value problem with fractional boundary condition”, Advancements In Mathematical Sciences (AMS 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, 020096  crossref  isi  scopus
    15. M. Kirane, B. T. Torebek, “On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions”, Math. Meth. Appl. Sci., 39:5 (2016), 1121–1128  crossref  mathscinet  zmath  isi  elib  scopus
    16. B. Kh. Turmetov, “On solvability of a boundary value problem for an inhomogeneous polyharmonic equation with a fractional order boundary operator”, Ufa Math. J., 8:3 (2016), 155–170  mathnet  crossref  mathscinet  isi  elib
    17. B. Turmetov, M. Koshanova, K. Usmanov, “Solvability of boundary-value problems for Poisson equations with hadamard type boundary operator”, Electron. J. Differ. Equ., 2016, 161  mathscinet  zmath  isi
    18. B. Turmetov, “On some boundary value problems for nonhomogenous polyharmonic equation with boundary operators of fractional order”, Acta Math. Sci., 36:3 (2016), 831–846  crossref  mathscinet  zmath  isi  scopus
    19. B. Kh. Turmetov, “On an exterior boundary value problem for the Laplace equation with boundary operator of fractional order”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040014  crossref  isi  scopus
    20. B. T. Torebek, B. Kh. Turmetov, “Questions on solvability of exterior boundary value problems with fractional boundary conditions”, Electron. J. Qual. Theory Differ., 2016, no. 25  crossref  mathscinet  isi  scopus
    21. V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Math. Notes, 102:1 (2017), 31–42  mathnet  crossref  crossref  mathscinet  isi  elib
    22. Turmetov B., Nazarova K., “on Fractional Analogs of Dirichlet and Neumann Problems For the Laplace Equation”, Mediterr. J. Math., 16:3 (2019), 59  crossref  mathscinet  zmath  isi  scopus
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