Synchronization Analysis for a Class of Proportional Caputo Fractional-Order Neural Networks

This paper investigates the synchronization problem for a class of proportional Caputo fractional-order neural networks with respect to another function. A master–slave framework is formulated, and a linear state-feedback controller is proposed for the response system. Under a standard Lipschitz condition on the activation functions, sufficient conditions ensuring the convergence of the synchronization error to zero are established. The analysis is based on an explicit integral representation of the error system, a generalized Gronwall-type inequality, and asymptotic properties of the Mittag–Leffler function. The obtained criterion explicitly reveals the roles of the fractional order, the proportional parameter, the control gain, and the network interconnection matrix. Numerical experiments based on a benchmark fractional Hopfield neural network illustrate the effectiveness of the proposed approach. In particular, a scaled benchmark satisfying all theoretical assumptions provides a strict validation of the main theorem, while the original benchmark highlights the conservative nature of the derived sufficient conditions.