The existence and averaging principle for stochastic fractional
differential equations with impulses
Abstract
In this paper, a class of stochastic fractional differential equations
(SFDEs) with impulses is considered. By virtue of the Monch’s fixed
point theorem and Banach contraction principle, we explore the existence
and uniqueness of solutions to the addressed system. Furthermore, with
the aid of the Jensen’s inequality, Holder inequality,
Burkholder-Davis-Gundy inequality, Gronwall-Bellman inequality and some
novel assumptions, the averaging principle of our considered system is
obtained. At the end of this paper, an example is provided to illustrate
the theoretical results.