Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems

•The global Mittag–Leffler ultimate bounds and synchronization for fractional order plasma chaotic systems are studied.•Some new ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds are derived via generalized Lyapunov function theory.•Linear feedback control tactics with two inputs or one input as well as fractional order adaptive control with one input are proposed.•The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. This paper focuses on the Mittag–Leffler ultimate bounds (MLUBs) and synchronization of fractional-order plasma chaotic systems (FOPCSs). For one thing, by choosing some appropriate generalized Lyapunov functions and combining fractional-order differential inequalities, some new estimates on the 3D ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds for the FOPCS are acquired according to system parameters, which perfect the previous studies and may infer a few new estimates. For another, linear feedback control tactics with two inputs or one input as well as fractional-order adaptive control with one input and a single variable are presented to realize the synchronization of two FOPCSs. Several new sufficient conditions for synchronization are analytically obtained by using inequality methods. The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. Finally, numerical simulations are shown to confirm the correctness of the presented synchronization schemes.