S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations

Shufen Zhao; Xiaoqian Li; Jianzhong Zhang; Shufen Zhao; Xiaoqian Li; Jianzhong Zhang

doi:10.3934/era.2023029

Electronic Research Archive

2023, Volume 31, Issue 2: 599-614. doi: 10.3934/era.2023029

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Research article

S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations

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

Received: 06 August 2022 Revised: 12 October 2022 Accepted: 17 October 2022 Published: 15 November 2022

In this paper, we introduce the concept of an S-asymptotically $ \omega $-periodic process in distribution for the first time, and by means of the successive approximation and the Banach contraction mapping principle, respectively, we obtain sufficient conditions for the existence and uniqueness of the S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations.
Citation: Shufen Zhao, Xiaoqian Li, Jianzhong Zhang. S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations[J]. Electronic Research Archive, 2023, 31(2): 599-614. doi: 10.3934/era.2023029

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Abstract

In this paper, we introduce the concept of an S-asymptotically $ \omega $-periodic process in distribution for the first time, and by means of the successive approximation and the Banach contraction mapping principle, respectively, we obtain sufficient conditions for the existence and uniqueness of the S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations.

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