Modelling, analysis and simulations of some chaotic systems using derivative with Mittag–Leffler kernel.

• Several chaotic systems with interesting behaviors are presented. • Atangana–Baleanu fractional derivative operator is considered. • Existence and uniqueness of general system as well as local stability analysis are examined. • A range of chaotic patterns examined through time series are obtained for different instances of fractional orders. In this paper, a range of chaotic systems with some interesting behaviors such as multi-scroll attractors, self-excited and hidden attractors, period-doubling to chaos, periodic and chaotic bursting oscillations, and different multiple coexisting attractors have been considered and modelled with the new Atangana–Baleanu fractional derivative operator in time. Existence and uniqueness of general system as well as local stability analysis are examined. In the simulation framework, a range of chaotic patterns examined through time series were obtained for different instances of fractional orders. Comparison between the integer (with p = 1) and noninteger (0 < p < 1) order results are given. [ABSTRACT FROM AUTHOR]