<p>This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of various time-fractional functional differential equations, particularly those exhibiting Mittag-Leffler stability. Our primary analytical framework relies on the sub-additivity property of the Mittag-Leffler function and its optimal asymptotic decay rate estimation. These results refine and extend existing findings in the literature. We demonstrate the significance of this fractional Halanay-type inequality through two key applications. First, by integrating our results with the positive representation method for delay differential systems, we establish an asymptotic stability criterion for a class of linear fractional coupled systems with bounded delays. This criterion transcends the traditional boundaries of positive system theory, offering a novel perspective on stability analysis. Second, utilizing energy estimates, we establish the contractivity and dissipativity for a class of time-fractional neutral functional differential equations. Our analysis highlights the characteristic long-term polynomial decay inherent in time-fractional evolutionary equations, thereby providing a rigorous theoretical foundation for subsequent numerical investigations.</p>