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

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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.

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Authors and Affiliations

  1. South-Ural State University, Chelyabinsk, 454080, Russia

    V. V. Karachik

  2. Kh. Yasavi International Kazakh-Turkish University, Turkestan, Kazakhstan

    B. Kh. Turmetov & B. T. Torebek

Authors
  1. V. V. Karachik
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  2. B. Kh. Turmetov
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  3. B. T. Torebek
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Correspondence to V. V. Karachik.

Additional information

Original Russian Text © V. V. Karachik, B. Kh. Turmetov, and B. T. Torebek, 2011, published in Matematicheskie Trudy, 2011, Vol. 14, No. 1, pp. 99–125.

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Karachik, V.V., Turmetov, B.K. & Torebek, B.T. On some integro-differential operators in the class of harmonic functions and their applications. Sib. Adv. Math. 22, 115–134 (2012). https://doi.org/10.3103/S1055134412020046

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  • DOI: https://doi.org/10.3103/S1055134412020046

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