The averaging principle for Caput type fractional stochastic differential equations with Lévy noise

In this paper, we study the averaging principle for Caputo type fractional stochastic differential equations with Lévy noise. Firstly, the estimate on higher moments for the solution is given. Secondly, under some suitable assumptions, we show that the solutions of original equations can be approximated by the solutions of averaged equations in the sense of pth moment and convergence in probability by Hölder inequality. Finally, a simulation example is given to verify the theoretical results.