Dynamic stability of a class of fractional‐order nonlinear systems via fixed point theory
Xin Liu, Lili Chen, Yanfeng Zhao, Xianhua Song · Mathematical Methods in the Applied Sciences · 2021
In this paper, the problem of the uniform stability for a class of fuzzy fractional‐order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in . However, the case of the fractional‐order belonging to has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.