A fractionally loaded boundary value problem two-dimensional in the spatial variable
Кеңiстiктiк айнымалыдағы екi өлшемдi бөлшектiк жүктемелi шеттiк есеп
Дробно-нагруженная краевая задача, двумерная по пространственной переменной
Kosmakova M.T. Izhanova K.A. Kasymova L.Zh.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 272 - 83 pp.
In the paper, the boundary value problem for the loaded heat equation is solved, and the loaded term is represented as the Riemann-Liouville derivative with respect to the time variable. The domain of the unknown function is the cone. The order of the derivative in the loaded term is less than 1, and the load moves along the lateral surface of the cone, that is in the domain of the desired function. The boundary value problem is studied in the case of the isotropy property in an angular coordinate (case of axial symmetry). The problem is reduced to the Volterra integral equation, which is solved by the method of the Laplace integral transformation. It is also shown by direct verification that the resulting function satisfies the boundary value problem.
heat equation , isotropy , Laplace transformation , loaded boundary value problem , Volterra integral equation
Text of the article Перейти на текст статьи
Karaganda University of the name of academician E.A. Buketov, Institute of Applied Mathematics, Karaganda, Kazakhstan
Abylkas Saginov Karaganda Technical University, Karaganda, Kazakhstan
Karaganda University of the name of academician E.A. Buketov
Abylkas Saginov Karaganda Technical University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026