Hilfer fractional stochastic system driven by mixed Brownian motion and Lvy noise suffered by non-instantaneous impulses

Abstract

This paper discusses the existence result for a class of non-instantaneous impulsive Hilfer fractional stochastic systems (NIHFSS) driven by mixed Brownian motion and Lvy noise. Sufficient conditions are obtained by utilizing Mnch fixed point theorem (FPT) for the existence of solution of non-instantaneous impulsive Hilfer fractional stochastic system of order and of type The existence result is derived by adapting stochastic analysis techniques, the measure of non-compactness, semigroup theory, and fractional calculus. The discussed theory is illustrated through an example.