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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 752–764 (Mi smj2361)  

This article is cited in 14 scientific papers (total in 14 papers)

Some properties and applications of the integrodifferential operators of Hadamard–Marchaud type in the class of harmonic functions

A. S. Berdysheva, B. Kh. Turmetovb, B. J. Kadirkulovc

a Kazakh National Pedagogical University, Almaty, Kazakhstan
b Kh. Yasavi International Kazakh-Turkish University, Turkestan, Kazakhstan
c Tashkent State Institute of Oriental Studies, Tashkent, Uzbekistan

Abstract: In the class of harmonic functions, we study the properties of some integrodifferential operators generalizing the operators of fractional derivation in the sense of Hadamard and Hadamard–Marchaud. By way of application of the so-obtained properties, we consider some boundary value problems for the Laplace equation in the ball.

Keywords: Laplace equation, integrodifferential operator, operators of fractional derivation in the sense of Hadamard and Hadamard–Marchaud.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 600–610

Bibliographic databases:

UDC: 517.956
Received: 26.03.2011

Citation: 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”, Sibirsk. Mat. Zh., 53:4 (2012), 752–764; Siberian Math. J., 53:4 (2012), 600–610

Citation in format AMSBIB
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\paper Some properties and applications of the integrodifferential operators of Hadamard--Marchaud type in the class of harmonic functions
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 4
\pages 752--764
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\jour Siberian Math. J.
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\vol 53
\issue 4
\pages 600--610
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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. 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
    2. B. J. Kadirkulov, “Boundary problems for mixed parabolic-hyperbolic equations with two lines of changing type and fractional derivative”, Electron. J. Differ. Equ., 2014, 57  mathscinet  zmath  isi  elib
    3. 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
    4. 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  mathscinet  zmath  isi  elib  scopus
    5. M. A. Sadybekov, B. Kh. Turmetov, M. A. Muratbekova, “On solvability of some nonlocal boundary value problems with the Hadamard boundary operator”, International Conference on Analysis and Applied Mathematics (ICAAM 2014), AIP Conf. Proc., 1611, eds. A. Ashyralyev, E. Malkowsky, Amer. Inst. Phys., 2014, 266–270  crossref  mathscinet  isi  scopus
    6. 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
    7. 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  mathscinet  zmath  isi  elib  scopus
    8. 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
    9. 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
    10. 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
    11. I. I. Bavrin, O. E. Iaremko, “Inverting of generalized Riemann–Liouville operator by means of integral Laplace transform”, Ufa Math. J., 8:3 (2016), 41–48  mathnet  crossref  mathscinet  isi  elib
    12. 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
    13. 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
    14. 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
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