Effects of Lévy noise and impulsive action on the averaging principle of Atangana–Baleanu fractional stochastic delay differential equations

Abstract

Abstract As delays are common, persistent, and ingrained in daily life, it is imperative to take them into account. In this work, we explore the averaging principle for impulsive Atangana–Baleanu fractional stochastic delay differential equations driven by Lévy noise. The link between the averaged equation solutions and the equivalent solutions of the original equations is shown in the sense of mean square. To achieve the intended outcomes, fractional calculus, semigroup properties, and stochastic analysis theory are used. We also provide an example to demonstrate the practicality and relevance of our research.

Keywords

• Delay stochastic differential equation
• Lévy noise
• Fractional derivative
• Impulsive