Mittag-Leffler ultimate boundedness of fractional-order nonautonomous delay systems

This paper investigates the Mittag-Leffler ultimate boundedness of fractional-order nonautonomous systems with delay. First, using the properties of the Mittag-Leffler function and the fractional-order comparison principle, a novel fractional-order nonautonomous Halanay inequality is proposed, which no longer requires the conditions of boundedness and common factors of the coefficients of the systems. This implies that the conditions are less conservative than the existing results. Then, with the help of the obtained inequality, some criteria for the Mittag-Leffler ultimate boundedness of the considered system are derived. Finally, examples are given to demonstrate the effectiveness of the findings.