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Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses. (English) Zbl 1484.34169

Summary: 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 \(0 < \beta < 1\) and type \(0 \leq\alpha\leq 1\) 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.

MSC:

34K30 Functional-differential equations in abstract spaces
34K37 Functional-differential equations with fractional derivatives
34K45 Functional-differential equations with impulses
34K50 Stochastic functional-differential equations
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