Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses

Abstract

The aim of this manuscript is to investigate the existence of mild solution of Hilfer fractional neutral stochastic differential equations (HFNSDEs) with non-instantaneous impluses. We establish a new criteria to guarantee the sufficient conditions for a class of HFNSDEs with non-instantaneous impluses of order 0 < β < 1 and type 0 ≤ α ≤ 1 is derived with the help of semigroup theory and fixed point approach, namely Mönch fixed point theorem. Finally, a numerical example is provided to validate the theoretical results. © 2021 the Author(s), licensee AIMS Press.