Electron. J. Diff. Equ., Vol. 2016 (2016), No. 161, pp. 1-12.

Solvability of boundary-value problems for Poisson equations with Hadamard type boundary operator

Batirkhan Turmetov, Maira Koshanova, Kayrat Usmanov

Abstract:
In this article we study properties of some integro-differential operators of fractional order. As an application of the properties of these operators for Poisson equation we examine questions on solvability of a fractional analogue of Neumann problem and analogues of periodic boundary-value problems for circular domains. The exact conditions for solvability of these problems are found.

Submitted December 21, 2015. Published June 27, 2016.
Math Subject Classifications: 35J05, 35J25, 34B10, 26A33.
Key Words: Fractional derivative; Hadamard operator; Poisson equation; Neumann problem.

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Batirkhan Kh. Turmetov
Department of Mathematics
Akhmet Yasawi International Kazakh-Turkish University
161200 Turkistan, Kazakhistan
email: batirkhan.turmetov@ayu.edu.kz
Maira D. Koshanova
Department of Mathematics
Akhmet Yasawi International Kazakh-Turkish University
161200 Turkistan, Kazakhistan
email: maira_koshanova@mail.ru
Kayrat I. Usmanov
Department of Mathematics
Akhmet Yasawi International Kazakh-Turkish University
161200 Turkistan, Kazakhistan
email: y_kairat@mail.ru

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