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.

中文翻译：

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Atangana–Baleanu分数阶线性系统的有限时间稳定性

本文研究了Atangana–Baleanu分数导数框架中的分数阶线性系统。首先，我们证明Caputo分数导数的某些性质在AB分数导数的意义上也成立。随后，导出了几个足以保证系统的有限时间稳定性和有限时间有界性的准则。最后，通过一个例子来说明我们主要结果的有效性。