The S-asymptotically $ \omega $-periodic solutions for stochastic fractional differential equations with piecewise constant arguments

Shufen Zhao; Shufen Zhao

doi:10.3934/era.2023361

Electronic Research Archive

2023, Volume 31, Issue 12: 7125-7141. doi: 10.3934/era.2023361

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The S-asymptotically $ \omega $-periodic solutions for stochastic fractional differential equations with piecewise constant arguments

Shufen Zhao ^,

School of Mathematics and Statistics, Taishan University, Taian 271000, China

Received: 10 July 2023 Revised: 25 October 2023 Accepted: 26 October 2023 Published: 08 November 2023

In this paper, two kinds of stochastic differential equations with piecewise constant arguments are investigated. Sufficient conditions for the existence of the square-mean S-asymptotically $ \omega $-periodic solutions of these two type equations are derived where $ \omega $ is an integer. Then, the global asymptotic stability for one of them is considered by using the comparative approach. In order to show the theoretical results, we give two examples.
- square-mean S-asymptotically $ \omega $-periodic solution,
- Lévy noise,
- piecewise constant argument
Citation: Shufen Zhao. The S-asymptotically $ \omega $-periodic solutions for stochastic fractional differential equations with piecewise constant arguments[J]. Electronic Research Archive, 2023, 31(12): 7125-7141. doi: 10.3934/era.2023361

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Abstract

In this paper, two kinds of stochastic differential equations with piecewise constant arguments are investigated. Sufficient conditions for the existence of the square-mean S-asymptotically $ \omega $-periodic solutions of these two type equations are derived where $ \omega $ is an integer. Then, the global asymptotic stability for one of them is considered by using the comparative approach. In order to show the theoretical results, we give two examples.

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