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Keywords = ψ-Capuo fractional stochastic delay differential equations

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15 pages, 350 KiB  
Article
Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps
by Dandan Yang, Jingfeng Wang and Chuanzhi Bai
Symmetry 2023, 15(7), 1346; https://doi.org/10.3390/sym15071346 - 1 Jul 2023
Cited by 6 | Viewed by 1622
Abstract
In this paper, we study the averaging principle for ψ-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequality, and the Ho¨lder inequality, we prove that the solution of the [...] Read more.
In this paper, we study the averaging principle for ψ-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequality, and the Ho¨lder inequality, we prove that the solution of the averaged FSDDEs converges to that of the standard FSDDEs in the sense of Lp. Our result extends some known results in the literature. Finally, an example and simulation is performed to show the effectiveness of our result. Full article
(This article belongs to the Special Issue Applied Mathematics and Fractional Calculus II)
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