An effective averaging theory for fractional neutral stochastic equations of order 0<α<1 with Poisson jumps

This paper, focusing on the fractional neutral stochastic differential equations (FNSDEs) in the Euclidean space Rⁿ, successfully provides the first evidence of a new fractional averaging theorem via rigorous mathematical deductions. With the help of integration by part, the fractional term is handled simply and ingeniously. Based on this new idea, we show that the mild solutions of two fractional systems before and after averaging are equivalent in mean square sense. The study here gives a general approach to come up with the Khasminskii averaging principle for FNSDEs.