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

Abstract

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 γ satisfies 0<γ<1 and 1<γ<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.