The averaging principle for stochastic differential equations with Caputo fractional derivative

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This paper presents an averaging principle for Caputo fractional stochastic differential equations (FSDEs) driven by Brown motion. Under some assumptions, the solutions to FSDEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. The analyses of solutions to systems before and after averaging, allow to extend the classical Khasminskii approach to Caputo fractional stochastic equations.