Asymptotics solutions of a singularly perturbed integro-differential fractional order derivative equation with rapidly oscillating coefficients
Жылдам осцилляцияланатын коэффициенттi бөлшек реттi туындылы сингуляр ауытқыған интегро-дифференциалдық теңдеудiң асимптотикасы
Асимптотика решений сингулярно-возмущенного интегро-дифференциального уравнения дробного порядка с быстро осциллирующими коэффициентами
Bobodzhanova M.A. Kalimbetov B.T. Bekmakhanbet G.M.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#104Issue 456 - 67 pp.
In this paper, the regularization method of S.A.Lomov is generalized to the singularly perturbed integro-differential fractional-order derivative equation with rapidly oscillating coefficients. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution to this problem. The case of the absence of resonance is considered, i.e. the case when an integer linear combination of a rapidly oscillating inhomogeneity does not coincide with a point in the spectrum of the limiting operator at all points of the considered time interval. The case of coincidence of the frequency of a rapidly oscillating inhomogeneity with a point in the spectrum of the limiting operator is called the resonance case. This case is supposed to be studied in our subsequent works. More complex cases of resonance (for example, point resonance) require more careful analysis and are not considered in this work.
fractional order derivation , integro-differential equation , iterative problems , singularly perturbed , solvability of iterative problems
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National Research University, Moscow Power Engineering Institute, Moscow, Russian Federation
Kh.A. Yasawi International Kazakh-Turkish University, Turkestan, Kazakhstan
National Research University
Kh.A. Yasawi International Kazakh-Turkish University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026