Finite Time Stability of Caputo-Katugampola Fractional Order Fuzzy Cellular Neural Networks with Time Delay and Multi-Proportional Delays

In this paper, the finite time stability problem are investigated for a class of Caputo-Katugampola fractional order fuzzy cellular neural networks with time delay and multi-proportional delays. Based on contraction mapping principle, the generalized Gronwall inequality, Hölder’s inequality and techniques of iteration, finite time stability results of the equilibrium point for the addressed system are obtained. The novelty lies in the simultaneous consideration of hybrid delays and the adoption of the more general Caputo-Katugampola derivative. Numerical simulations are conducted to validate the theoretical results. Furthermore, comparative analyses are provided to illustrate the influence of fractional orders and scaling parameters on the system’s convergence behavior. The results demonstrate that the proposed criteria are effective and possess broader applicability in modeling complex neural systems.