Relative Controllability of Nonlinear Fractional Langevin Systems with Delays in Control

This paper is concerned with the relative controllability of fractional Langevin dynamical systems with both multiple delays and distributed delays in control for finite dimensional spaces. Sufficient conditions for the controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag–Leffler matrix function. Examples are provided to illustrate the theory.