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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.
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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
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\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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http://mi.mathnet.ru/eng/mt208 http://mi.mathnet.ru/eng/mt/v14/i1/p99
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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B. Kh. Turmetov, “Solvability of fractional analogues of the Neumann problem for a nonhomogeneous biharmonic equation”, Electron. J. Differ. Equ., 2015, 82
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B. Kh. Turmetov, B. T. Torebek, “Modified Bavrin operators and their applications”, Differ. Equ., 51:2 (2015), 243–254
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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
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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
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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
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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
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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
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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
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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
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V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Math. Notes, 102:1 (2017), 31–42
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Turmetov B., Nazarova K., “on Fractional Analogs of Dirichlet and Neumann Problems For the Laplace Equation”, Mediterr. J. Math., 16:3 (2019), 59
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