Relatively exact controllability of fractional stochastic delay system
driven by Lévy noise
Abstract
In this article, we consider the relatively exact controllability of
fractional stochastic delay system (FSDS) driven by Lévy noise. Firstly,
we derive the solution of linear FSDS via delayed matrix functions of
Mittag-Leffler (M-L). Subsequently, by virtue of the controllability
Grammian matrix, we explore the relatively exact controllability of
linear FSDS. In addition, with the aid of Jensen’s inequality, Hölder’s
inequality and Itô’s isometry, the existence and uniqueness of the
considered nonlinear FSDS are investigated by employing Banach
contraction principle.Thereafter, the relatively exact controllability
of nonlinear FSDS is discussed. Finally, the theoretical results are
supported through an example.