Well posedness of second-order impulsive fractional neutral stochastic differential equations

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

doi:10.3934/math.2021536

AIMS Mathematics

2021, Volume 6, Issue 9: 9222-9235. doi: 10.3934/math.2021536

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Research article

Well posedness of second-order impulsive fractional neutral stochastic differential equations

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: 04 March 2021 Accepted: 24 May 2021 Published: 21 June 2021
MSC : 34K30, 60H60

In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space. Firstly, sufficient conditions of the existence and the uniqueness of the mild solution for this type of equations are driven by means of the successive approximation and the Bihari's inequality. Next we get the stability in mean square of the mild solution via continuous dependence on initial value.
- stochastic fractional differential equations,
- Bihari's inequality,
- successive approximation,
- Poisson jumps
Citation: Ramkumar Kasinathan, Ravikumar Kasinathan, Dumitru Baleanu, Anguraj Annamalai. Well posedness of second-order impulsive fractional neutral stochastic differential equations[J]. AIMS Mathematics, 2021, 6(9): 9222-9235. doi: 10.3934/math.2021536

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Abstract

In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space. Firstly, sufficient conditions of the existence and the uniqueness of the mild solution for this type of equations are driven by means of the successive approximation and the Bihari's inequality. Next we get the stability in mean square of the mild solution via continuous dependence on initial value.

References

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