Averaging principle for fractional stochastic differential equations with L^p convergence

In this paper, we prove the averaging principle for fractional stochastic differential equations (FSDEs) in the sense of L^p (pth moment) with inequality techniques. The solution of the averaged FSDEs converges to that of the standard FSDEs in the sense of L^p, which is a generalization of the existing result (p=2) of the averaging principle for FSDEs. A numerical example is constructed to illustrate the correctness of the theoretical result. In addition, we correct the mistakes in the proof of Xu et al. (2019. 2020) and Luo et al. (2021).