On the Averaging Principle of Caputo Type Neutral Fractional Stochastic Differential Equations

In this manuscript, we study the averaging principle for a class of neutral fractional stochastic differential equations. Firstly, the existence and uniqueness of solution are discussed by applying the principle of contraction mapping. Secondly, the averaging principle in the sense of Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}$$\end{document} is studied by using the Jensen’s inequality, Hölder inequality, Burkholder–Davis–Gundy inequality, Grönwall–Bellman inequality and interval translation technique. In addition, we give an example and numerical simulations to analyze the theoretical results.