This paper addresses the finite-time stability of generalized neutral fractional systems with time delays. Firstly, the bivariate Mittag-Leffler type matrix function is introduced and some new estimations for the Mittag-Leffler function in terms of the exponential function are deduced. Additionally, based on the $\rho$-Laplace transform, the properties of the Mittag-Leffler function and the generalized Gronwall inequality, a new criterion on finite-time stability is obtained. Finally, a numerical example is hence proposed to validate theoretical findings.

中文翻译：

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具有时滞的广义中立分数阶微分系统的稳定性分析

本文讨论了具有时滞的广义中立分数系统的有限时间稳定性。首先，介绍了二元Mittag-Leffler型矩阵函数，并根据指数函数推导了Mittag-Leffler函数的一些新估计。此外，根据$\rho$-Laplace变换，Mittag-Leffler函数的性质和广义的Gronwall不等式，获得了有关有限时间稳定性的新准则。最后，因此提出了一个数值例子来验证理论发现。