Asymptotic Solutions of a Singularly Perturbed Integro-Differential Fractional Order Derivative Equation with Rapidly Oscillating Coefficients

Open Access

Original research article

Author(s):

M. Akylbayev^a, B. Kalimbetov^b, D. Zhaidakbayeva^c

^a Department of Mathematics, A. Kuatbekov Peoples’ Friendship University, Shymkent, Kazakhstan.
^b Department of Mathematics, M. Auezov South Kazakhstan University, A. Kuatbekov Peoples’ Friendship University, Shymkent, Kazakhstan.
^c Department of Mathematics, M. Auezov South Kazakhstan University, Shymkent, Kazakhstan.

Advances in the Theory of Nonlinear Analysis and its Applications 7(2), 441-454.

Received: January 15, 2023

Accepted: May 28, 2023

Published: June 15, 2023

Abstract

In this paper, the regularization method of S.A. Lomov is generalized to singularly perturbed integro-differential fractional order derivative equations with rapidly oscillating coefficients. The main purpose of the study is to reveal the influence of the integral term and rapidly oscillating coefficients on the asymptotic behavior of the solution of the original problem.

To study the influence of rapidly oscillating coefficients on the leading term of the asymptotic solutions, we consider a simple case — namely, the case of no resonance (when an entire linear combination of frequencies of a rapidly oscillating cosine does not coincide with the frequency of the spectrum of the limit operator).

Keywords: Singularly perturbed, fractional order derivation, integro-differential equation, rapidly oscillating coefficients, iterative problems.

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APA Style

Akylbayev, M., Kalimbetov, B., & Zhaidakbayeva, D. (2023). Asymptotics Solutions of a Singularly Perturbed Integro-differential Fractional Order Derivative Equation with Rapidly Oscillating Coefficients. Advances in the Theory of Nonlinear Analysis and its Application , 7 (2), 441-454.