The Averaging Principle for Caputo Type Fractional Stochastic Differential Equations with Lévy Noise

Abstract

In this paper, the averaging principle for Caputo type fractional stochastic differential equations with Lévy noise is investigated with consideration of a new method for dealing with singular integrals. Firstly, the estimate on higher moments for the solution is given. Secondly, under some suitable assumptions, we prove the averaging principle for Caputo type fractional stochastic differential equations with Lévy noise by using the Hölder inequality. Finally, a simulation example is given to verify the theoretical results.

Keywords

• averaging principle
• Caputo fractional derivative
• stochastic differential equations
• Lévy noise
• <i>p</i>th moment