Averaging Principle for <i>ψ</i>-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

Abstract

In this paper, we study the averaging principle for ψ-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequality, and the Ho¨lder inequality, we prove that the solution of the averaged FSDDEs converges to that of the standard FSDDEs in the sense of Lp. Our result extends some known results in the literature. Finally, an example and simulation is performed to show the effectiveness of our result.

Keywords

• averaging principle
• <i>ψ</i>-Capuo fractional stochastic delay differential equations
• Poisson jumps
• <i>L^p</i> convergence