Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses - Kasinathan, Ramkumar; Kasinathan, Ravikumar; Baleanu, Dumitru; Annamalai, Anguraj (AIMS mathematics, 2021)
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.