Mittag–Leffler Stability of a Switched Fractional Gene Regulatory Network Model with a Short Memory

Ravi P. Agarwal, Snezhana Hristova () and Donal O’Regan
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Ravi P. Agarwal: Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
Snezhana Hristova: Faculty of Mathematics and Informatics, Plovdiv University, 4000 Plovdiv, Bulgaria
Donal O’Regan: School of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, Ireland

Mathematics, 2025, vol. 13, issue 22, 1-22

Abstract: A model of gene regulatory networks with generalized Caputo fractional derivatives with respect to another function is set up in this paper. The main characteristic of the model is the presence of a switching rule, which changes at certain times at both the lower limit of the applied fractional derivative and the right-side part of the equations. This gives the opportunity for better and more adequate modeling of the problem. Mittag–Leffler-type stability is defined for the model and studied with two types of Lyapunov functions. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are given, and two types of sufficient conditions are obtained. An example is provided to illustrate our theoretical results and the influences of the type of fractional derivative as well the switching rule on the stability behavior of the equilibrium.

Keywords: gene regulatory networks; generalized Caputo fractional derivatives with respect to other functions; nonlinear switched systems; Mittag–Leffler-type stability; Lyapunov functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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