On the non-uniqueness of the solution to a boundary value problem of heat conduction with a load in the form of a fractional derivative
Kosmakova M.T. Izhanova K.A. Khamzeyeva A.N.
2022E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2022#108Issue 498 - 106 pp.
The paper deals with the second boundary value problem for the loaded heat equation in the first quadrant. The loaded term contains a fractional derivative in the Caputo sense of an order α, 2 < α < 3. The boundary value problem is reduced to an integro-differential equation with a difference kernel by inverting the differential part. It is proved that a homogeneous integro-differential equation has at least one non-zero solution. It is shown that the solution of the homogeneous boundary value problem corresponding to the original boundary value problem is not unique, and the load acts as a strong perturbation of the boundary value problem.
Caputo fractional derivative , loaded equation , non-unique solvability , second boundary value problem , strong perturbation
Text of the article Перейти на текст статьи
Karagandy University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
Karagandy University of the name of academician E.A. Buketov
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026