Averaging principle for non‐Lipschitz fractional stochastic evolution equations with random delays modulated by two‐time‐scale Markov switching processes

Abstract

In the paper, we consider the averaging principle for a class of fractional stochastic evolution equations with random delays modulated by a two‐time‐scale continuous‐time Markov chain under the non‐Lipschitz coefficients, which extends the existing results: from Lipschitz to non‐Lipschitz case, from classical to fractional equations, from constant to random delays. Using ‐order fractional resolvent operator theory and stopping time technique, a general theorem on the existence and uniqueness of mild solutions is obtained first; further, strong averaging principle for fractional stochastic delay evolution equation is investigated, which simplifies the original system.