A new investigation of impulsive fractional stochastic delayed systems in the framework of $ (\delta, \psi) $-Hilfer derivative and Lévy processes

Abstract

In this paper, the averaging result for impulsive $ (\delta, \psi) $-Hilfer fractional stochastic delayed differential equations (FSDDEs) caused by the Lévy process was derived. In the sense of mean square, the relationship between the equivalent solutions of the original equations and the averaged equation solutions was demonstrated. Our findings allowed us to shift our attention from the original, more complicated system to the averaged system. Additionally, to demonstrate the relevance and practicality of our findings, an example was given.