Abstract
In this paper, we consider controllability of nonlinear fractional delay dynamical systems with prescribed controls. We firstly give the solution representation of the fractional delay dynamical systems using Laplace transform and Mittag–Leffler functions. Then we give necessary and sufficient conditions for the controllability criteria of linear fractional delay dynamical systems with prescribed controls. Further, we use a fixed point theorem to establish the sufficient condition for the controllability of nonlinear fractional delay dynamical systems with prescribed controls. In particular, we determine several sufficient conditions on the nonlinear function term so that if the linear system is controllable, then the nonlinear system is controllable. Finally, we give two examples to demonstrate the applicability of our obtained results.
Highlights
Fractional calculus is a generalization of integer order calculus
Unlike the integer order calculus, the fractional calculus is defined by nonlocal operators
Fractional delay dynamical systems are an important kind of fractional order systems in real life
Summary
Fractional calculus is a generalization of integer order calculus. Unlike the integer order calculus, the fractional calculus is defined by nonlocal operators. Fractional delay dynamical systems are an important kind of fractional order systems in real life. In these years, some authors pay attention to the study about the fractional delay dynamical systems (for example, see [4, 9, 26, 34, 36]).
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