Abstract
This paper investigates a fractional-order linear system in the frame of Atangana–Baleanu fractional derivative. First, we prove that some properties for the Caputo fractional derivative also hold in the sense of AB fractional derivative. Subsequently, several sufficient criteria to guarantee the finite-time stability and the finite-time boundedness for the system are derived. Finally, an example is presented to illustrate the validity of our main results.
Highlights
Academic Editor: Atif Khan is paper investigates a fractional-order linear system in the frame of Atangana–Baleanu fractional derivative
In 2016, based on CF fractional derivatives, Atangana and Baleanu [9] introduced another new definition of fractional derivatives called AB fractional derivatives with a nonlocal and nonsingular kernel which are built by the generalized Mittag–Leffler function
Having the advantage of nonlocal and nonsingular kernel, AB fractional derivatives have been widely applied in many fields such as diffusion equation [19], electromagnetic waves in dielectric media [20], chaos [21], and circuit model [22]
Summary
Academic Editor: Atif Khan is paper investigates a fractional-order linear system in the frame of Atangana–Baleanu fractional derivative. E FTS and FTB for the fractional-order systems with α ∈ (0, 1) have been given in [24]. Motivated by the above works, this paper studies the FTS and FTB for the class of fractional-order LTI systems in the sense of this new type of AB fractional derivatives.
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