Khasminskii Approach for Conformable Stochastic Delay Differential Equations

This article aims to establish an averaging principle for conformable delay stochastic differential equations involving non‐Lipschitz coefficients. First, we derive Duhamel's formula utilizing standard cosine family of linear operators. Subsequently, by virtue of Picard iteration technique and contradiction method, we demonstrate the existence and uniqueness of mild solution for the considered system, respectively. Then under suitable averaging conditions, we prove that the solutions to the original equations can be approximated by the solutions to the averaged equations both in the sense of mean square and probability. It means that Khasminskii classical approach can be extended to stochastic differential equations of conformable type. As verification, an example is provided to illustrate the theoretical results.