Quadratic Lyapunov Functions for Stability of the Generalized Proportional Fractional Differential Equations with Applications to Neural Networks

A fractional model of the Hopfield neural network is considered in case application generalized proportional Caputo derivative. The stability analysis this used to show reliability processed information. An equilibrium defined, which generally not a constant (different than ordinary derivatives and Caputo-type derivatives). We define exponential Mittag–Leffler equilibrium. For this, we extend second method Lyapunov fractional-order establish useful inequality for derivative quadratic function. Several sufficient conditions are presented guarantee these types stability. Finally, two numerical examples illustrate effectiveness our theoretical results.