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The averaging principle of stochastic Hilfer fractional delay differential equations
  • Xinhai Xiao,
  • Jingli Xie
Xinhai Xiao
Jishou University
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Jingli Xie
Jishou University

Corresponding Author:[email protected]

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Abstract

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.
24 Aug 2024Submitted to Mathematical Methods in the Applied Sciences
28 Aug 2024Submission Checks Completed
28 Aug 2024Assigned to Editor
04 Sep 2024Review(s) Completed, Editorial Evaluation Pending
26 Oct 2024Reviewer(s) Assigned