The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

被引：2

作者：

Bai, Zhenyu ^{[1
]}

Bai, Chuanzhi ^{[2
]}

机构：

[1] Xian Jiaotong Liverpool Univ, XJTLU Wisdom Lake Acad Pharm, Suzhou 215123, Peoples R China

[2] Huaiyin Normal Univ, Dept Math, Huaian 223300, Peoples R China

来源：

AXIOMS | 2024年 / 13卷 / 01期

关键词：

stochastic fractional delay differential systems; delayed Mittag-Leffler-type matrix function; existence and uniqueness; averaging principle; L-p convergence; EQUATIONS;

D O I：

10.3390/axioms13010068

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo-type fractional stochastic delay differential systems(FSDDSs) with Poisson jumps by utilizing the delayed perturbation of the Mittag-Leffler function. Moreover, by using the Burkholder-Davis-Gundy inequality, Doob's martingale inequality, and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of L-p. Some known results in the literature are extended.

引用

页数：18

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