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 Mo¨nch fixed point theorem. Finally, a numerical example is provided to validate the theoretical results.

Keywords

• existence
• non-instantaneous impulsive equation
• hilfer fractional stochastic system
• semigroup theory
• m\ddot{o}nch fixed point theorem