Trajectory controllability of fractional dynamical systems

Abstract

In this paper, we discuss the trajectory controllability of linear and nonlinear fractional dynamical systems represented by the fractional differential equations in the sense of Caputo fractional derivative by using the Mittag–Leffler function and Gronwall–Bellman inequality. For the nonlinear system, we assume Lipschitz-type conditions on the nonlinearity. Examples are given to illustrate the theoretical results.