Synchronization of Delay Switched Fractional Cohen–Grossberg Neural Network Models

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons are modeled by generalized Caputo fractional derivatives with respect to another function (GCFDF). We consider a time-dependent delay and a switching rule in the model, which specifies when to switch the system at the initially given times. The switching rule is a piecewise constant function, and its points of discontinuity are the lower limits of the applied GCFDF on the corresponding intervals. We develop theoretical tools for GCFDF, starting with an important inequality for estimating that derivative on quadratic functions. We define the global Mittag–Leffler synchronization and obtain sufficient conditions based on the Lyapunov method, using a Razumikhin condition and quadratic functions.