Musabek Akylbayevaa, Burkhan Kalimbetovb, Nilufar Pardaevac
a Department of Mathematics, A. Kuatbekov Peoples’ Friendship University, Shymkent, Kazakhstan.
b Department of Mathematics, M. Auezov South Kazakhstan University, Shymkent, Kazakhstan.
c Department of Mathematics, Almalyk Branch of the NRTU MISA, Almalyk, Uzbekistan.
In this paper, Lomov’s regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and a rapidly oscillating inhomogeneity. The main goal of the study is to reveal the influence of a rapidly changing kernel on the structure of the asymptotic solution and to analyze the additional boundary functions generated by rapidly oscillating inhomogeneities.
Keywords: Singularly perturbed; Fractional order derivation; Integro-differential equation; Solvability of iterative problems; Rapidly oscillating inhomogeneity.
Akylbayev, M., Kalimbetov, B., & Pardaeva, N. (2023). Influence of rapidly oscillating inhomogeneities in the formation of additional boundary layers for singularly perturbed integro-differential systems. Advances in the Theory of Nonlinear Analysis and Its Application, 7(3), 1–13.