Delay-independent stability criteria for fractional order time delayed gene regulatory networks in terms of Mittag-Leffler function

This paper investigates the finite-time delay-free stability criteria for fractional-order gene regulatory networks (FOGRNs) with feedback regulation time delays. The existence of unique equilibrium points of considered systems is established based on the Banach fixed point theorem and Cauchy-Schwarz inequality. Further, when the order gamma satisfies 0 < gamma < 1 and 1 < gamma < 2, some novel delay-free sufficient conditions are derived to ensure the finite-time stability for addressing fractional order systems by using the ideas of generalized Gronwall-Bellman inequality, equivalent norm techniques, and Laplace transform. In the end, the article comes up with two numerical cases to manifest the applicability and superiority of the obtained theoretical results.