AUTHOREA
Log in
Sign Up
Browse Preprints
LOG IN
SIGN UP
Essential Site Maintenance
: Authorea-powered sites will be updated circa 15:00-17:00 Eastern on Tuesday 5 November.
There should be no interruption to normal services, but please contact us at
[email protected]
in case you face any issues.
Jingli Xie
Public Documents
1
The averaging principle of stochastic Hilfer fractional delay differential equations
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.