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., 2012, Volume 53, Number 4,Pages <nobr>752

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

A. S. Berdyshev^a, B. Kh. Turmetov^b, B. J. Kadirkulov^c

^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.

UDC: 517.956

Received: 26.03.2011