ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISSON EQUATION WITH FRACTIONAL-ORDER BOUNDARY OPERATORS

Turmetov B.Kh.
2024 Petrozavodsk State University

Problemy Analiza
2024 #13(31)Issue 3 118 - 134 pp.

In this paper, a non-local analogue of the Laplace operator is introduced using involution-type mappings. For the corresponding non-local analogue of the Poisson equation in the unit ball, two types of boundary-value problems are considered. In the studied problems, the boundary conditions involve fractional-order operators with derivatives of the Hadamard type. The first problem generalizes the well-known Dirichlet, Neumann, and Robin problems for fractional-order boundary operators. The second problem is a generalization of periodic and antiperiodic boundary-value problems for circular domains. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Exact conditions for solvability of the studied problems are found, and integral representations of the solutions are obtained.

Dirichlet problem , fractional derivative , Hadamard operator , Neumann problem , non-local equation , periodic problem

Text of the article Перейти на текст статьи

Khoja Akhmet Yassawi International Kazakh-Turkish University, 29 B. Sattarhanov ave., Turkistan, 161200, Kazakhstan
Alfraganus University, 2a Yukori Karakamish Str., Tashkent, 100190, Uzbekistan

Khoja Akhmet Yassawi International Kazakh-Turkish University
Alfraganus University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026