The averaging principle for stochastic differential equations with Lévy noise involving conformable fractional derivative

In this paper, the averaging principle for conformable fractional stochastic differential equations with Lévy noise is investigated. Initially, the averaging principle for classical Itô-type conformable fractional stochastic differential equations is presented. Subsequently, the averaging principle is extended to the case involving Lévy noise. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel, this study introduces a novel method to assess the error between the averaged stochastic equation and the original stochastic differential equations, thereby effectively addressing the challenge posed by singular kernels. Finally, a simulation example is provided to validate the theoretical analysis.