The averaging principle of stochastic Hilfer fractional delay
differential equations
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.