Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays

Date
2021-12-09
Authors
Stamova, Ivanka
Stamov, Gani
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract

This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of an almost periodic state of the model are investigated and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. In addition, sufficient conditions for the global Mittag–Leffler stability of the almost periodic solutions are proposed. To justify our findings a numerical example is also presented.

Description
Keywords
gene regulatory networks, fractional-order derivatives, time-varying delays, impulses, almost periodicity, Mittag–Leffler stability, Lyapunov method
Citation
Fractal and Fractional 5 (4): 268 (2021)
Department
Mathematics