Controllability of nonlinear stochastic fractional higher order dynamical systems

Abstract

Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.