Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses

• Published in: AIMS mathematics Vol. 6; no. 5; pp. 4474 - 4491
• Main Authors: Kasinathan, Ramkumar, Kasinathan, Ravikumar, Baleanu, Dumitru, Annamalai, Anguraj
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: existence; hilfer fractional stochastic system; m\ddot{o}nch fixed point theorem; non-instantaneous impulsive equation; semigroup theory
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021265

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.