Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel

Abstract

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

“…They significantly contribute in the analysis and design of control systems [17]. Recently, numerous researchers have investigated generalizing the fundamental controllability principles to the domain of fractional-order control systems, see [18][19][20], and the references cited therein.…”

On Controllability of Impulsive Fractional Integro-differential Nonlocal System with State

“…Recently, many authors investigated the controllability of fractional differential equations by using various techniques. In papers [16][17][18][19][20], the researchers discussed the controllability of various nonlinear fractional differential equations with the help of semigroup theory and fixed point theorems, as for the papers [21][22][23][24][25][26][27], the authors used Mittag-Leffler function and fixed point theorems to investigate controllability for fractional differential equations. Delay differential equations with state-dependent delay arise normally from the modelling of infectious disease transmission, the modelling of immune response systems and the modelling of respiration, where the delay is due to the time required to accumulate an appropriate dosage of infection or antigen concentration [28].…”