Controllability of higher-order fractional damped stochastic systems with distributed delay

Abstract

In this paper, the controllability analysis is proposed for both linear and nonlinear higher-order fractional damped stochastic dynamical systems with distributed delay in Hilbert spaces which involve fractional Caputo derivative of different orders. Based on the properties of fractional calculus, the fixed point technique, and the construction of controllability Gramian matrix, we establish the controllability results for the considered systems. Finally, examples are constructed to illustrate the applicability of obtained results.

Controllability of stochastic fractional systems involving state-dependent delay and impulsive effects

“…In the branch of qualitative characteristics of dynamical systems, controllability is an essential aspect. Many researchers have expanded the findings of nonlinear and linear systems from integer order to fractional order because of its significance [1,4,6,7]. Apart from these works, controllability problems of nonlinear and linear systems involving delay in control were reported in [32,37].…”