Asymptotics solutions of a singularly perturbed integro-differential fractional order derivative equation with rapidly oscillating inhomogeneity
Abstract
In this work, the algorithm of S.A. Lomov’s regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and with a rapidly oscillating inhomogeneity. The main goal of the research is to identify the influence of exponentially oscillating inhomogeneity on the structure of the asymptotics of the solution to the original problem. The case of absence of resonance is considered, i.e. the case when a rapidly oscillating inhomogeneity does not coincide with the spectrum point of the limit operator at all points of the considered time interval.
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