Relative controllability of fractional dynamical systems with delays in control

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

► The problem of controllability of fractional dynamical systems is investigated.
► Sufficient conditions for controllability are obtained.
► Fixed point theorems and the controllability Grammian matrix are used.