Abstract
In this paper, the regularization method of S.A. Lomov is generalized to singularly perturbed integro-differential fractional order derivative equation 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 asymptotics of the solution of the original problem. To study the influence of rapidly oscillating coefficients on the leading term of the asymptotics of solutions, we consider a simple case, i.e. 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).