Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses

Ramkumar Kasinathan; Ravikumar Kasinathan; Dumitru Baleanu; Anguraj Annamalai; Ramkumar Kasinathan; Ravikumar Kasinathan; Dumitru Baleanu; Anguraj Annamalai

doi:10.3934/math.2021265

AIMS Mathematics

2021, Volume 6, Issue 5: 4474-4491. doi: 10.3934/math.2021265

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Research article

Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses

1.
Department of Mathematics, PSG College of Arts & Science, Coimbatore, 641 046, India
2.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Balgat, Ankara, Turkey
3.
Institute of Space Sciences, Magurele-Bucharest, Romania
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 18 November 2020 Accepted: 05 February 2021 Published: 22 February 2021
MSC : 26A33, 34A08, 34A12, 34A37, 60H10

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 M$ \ddot{o} $nch fixed point theorem. Finally, a numerical example is provided to validate the theoretical results.
- existence,
- non-instantaneous impulsive equation,
- Hilfer fractional stochastic system,
- semigroup theory,
- M$ \ddot{o} $nch fixed point theorem
Citation: Ramkumar Kasinathan, Ravikumar Kasinathan, Dumitru Baleanu, Anguraj Annamalai. Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses[J]. AIMS Mathematics, 2021, 6(5): 4474-4491. doi: 10.3934/math.2021265

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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 < \beta < 1 $ and type $ 0\leq \alpha \leq 1 $ is derived with the help of semigroup theory and fixed point approach, namely M$ \ddot{o} $nch fixed point theorem. Finally, a numerical example is provided to validate the theoretical results.

References

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