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Xinhai Xiao
Xinhai Xiao

Public Documents 1
The averaging principle of stochastic Hilfer fractional delay differential equations
Xinhai Xiao
Jingli Xie

Xinhai Xiao

and 1 more

September 02, 2024
In this paper, we conduct a thorough analysis for a group of stochastic Hilfer fractional delay differential equations (SHFDDEs) with Lipschitz parameters. By introducing innovative theoretical conditions, we successfully establish the existence and uniqueness solutions using the Carath e ̵́ odory approximation approach. Furthermore, we deduce the average principle for accordingly system by employing H o ̵̈ lder’s inequality, Jensen’s inequality, It o ˆ isometric distance, and Gronwall’s inequality. Ultimately, two demonstrative examples are undertaken to substantiate the efficacy and practical applicability of our findings.

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