Caputo mean-square attractors for non-autonomous stochastic differential equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915798378872832 |
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| author | Zhang, Lijuan Huang, Jianhua Wang, Yejuan |
| author_facet | Zhang, Lijuan Huang, Jianhua Wang, Yejuan |
| contents | This paper investigates Caputo mean-square attractors for non-autonomous stochastic evolution systems. We first introduce the concept of Caputo mean-square attractors and then establish a sufficient criterion for existence of such attractors.As an application, we consider a non-autonomous Caputo fractional stochastic differential equation of order $α\in (\frac{1}{2},1)$ in $L^2(Ω; \mathbb{R}^d)$ with a driving system on a compact base space $P$ and tempered fractional noise.It is shown that this equation generates a Caputo mean-square random semi-dynamical system on $\mathfrak{C} \times P$ with a skew-product semi-flow structure,where $\mathfrak{C}$ denotes the space of continuous functions $f\in \mathbb{R}^{+}\rightarrow L^2(Ω; \mathbb{R}^d)$. Under suitable conditions, we prove that this semi-dynamical system admits a Caputo mean-square attractor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Caputo mean-square attractors for non-autonomous stochastic differential equations Zhang, Lijuan Huang, Jianhua Wang, Yejuan Dynamical Systems Probability This paper investigates Caputo mean-square attractors for non-autonomous stochastic evolution systems. We first introduce the concept of Caputo mean-square attractors and then establish a sufficient criterion for existence of such attractors.As an application, we consider a non-autonomous Caputo fractional stochastic differential equation of order $α\in (\frac{1}{2},1)$ in $L^2(Ω; \mathbb{R}^d)$ with a driving system on a compact base space $P$ and tempered fractional noise.It is shown that this equation generates a Caputo mean-square random semi-dynamical system on $\mathfrak{C} \times P$ with a skew-product semi-flow structure,where $\mathfrak{C}$ denotes the space of continuous functions $f\in \mathbb{R}^{+}\rightarrow L^2(Ω; \mathbb{R}^d)$. Under suitable conditions, we prove that this semi-dynamical system admits a Caputo mean-square attractor. |
| title | Caputo mean-square attractors for non-autonomous stochastic differential equations |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2602.13561 |