The first boundary value problem for the fractional diffusion equation in a degenerate angular domain
Бұрыштық жойылмалы аядағы бөлшектi диффузия теңдеуi үшiн бiрiншi шекаралық есеп
Первая краевая задача для дробного диффузионного уравнения в угловой вырождающейся области
Ramazanov M.I. Pskhu A.V. Omarov M.T.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#113Issue 1162 - 173 pp.
This article addresses the problems observed in branching fractal structures, where super-slow transport processes can occur, a phenomenon described by diffusion equations with a fractional time derivative. The characteristic feature of these processes is their extremely slow relaxation rate, where a physical quantity changes more gradually than its first derivative. Such phenomena are sometimes categorized as processes with “residual memory”. The study presents a solution to the first boundary problem in an angular domain degenerating into a point at the initial moment of time for a fractional diffusion equation with the Riemann-Liouville fractional differentiation operator with respect to time. It establishes the existence theorem of the problem under investigation and constructs a solution representation. The need for understanding these super-slow processes and their impact on fractal structures is identified and justified. The paper demonstrates how these processes contribute to the broader understanding of fractional diffusion equations, proving the theorem’s existence and formulating a solution representation.
angular domain , Carleman-Vekua equation , fractional calculus , general solution , kernel , parabolic cylinder , partial differential equation , Riemann-Lioville fractional operator , unique solution , weak singularity
Text of the article Перейти на текст статьи
Institute of Applied Mathematics, Karaganda Buketov University, 28 Universitetskaya street, Karaganda, 100028, Kazakhstan
A. D. of IAMA KBSC RAS, The Department of Fractional Calculus, The Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Center of RAS, st. Shortanova, 89 A, Kabardin-Balkar Republic, Nalchik, 360000, Russian Federation
Institute of Applied Mathematics
A. D. of IAMA KBSC RAS
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026