Stability of Caputa– Hadmmard Fractional Differential Nonlinear ControlSystem with Delay Riemann −Katugampola

This research examines the finite-time stability of a specific category of neural networks with fractional order. Using modified Gronwall inequality and estimations of Mittag–Leffler functions, we provide adequate requirements to guarantee the finite-time stability of neural models with Caputo fractional derivatives. In addition, we have also established insights about the asymptotic stability of fractional-order neural models ,this research examines the Finite-time stability of a specific fractional-order neural network using the "generalized Grunwald inequality". This study introduces the concept of finite-time stability for neural models with fractional derivatives. By utilizing the generalized Gronwall inequality and estimates of Mittag-Leffler functions, sufficient conditions are derived to guarantee the finite-time stability of these models. The study also establishes results regarding the asymptotical stability of fractional-order neural models,our results suggest that our conclusions are more precise than the current literature on stability requirements, and we provide examples demonstrating the proposed theory's significance