Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays

This paper focuses on studying the quasi-uniform (Q-U) synchronization on fractional-order fuzzy neural networks (FOFNNs) with the proportional and distributed delays. The impacts of the Caputo derivative order, coefficients of network system and control gain constants on the synchronization performance are taken into account. Two novel time-dependent and Caputo derivative order-dependent algebraic criteria on the Q-U synchronization of FOFNNs are established by using Cauchy–Schwartz inequality, Minkowski inequality, Cp inequality and Hölder inequality, which reveal the internal influences of the time and fractional derivative order on Q-U synchronization with the derivative order interval (0,2). The simulation examples further confirm the effectiveness and practicability of the algebraic criteria in terms of the MATLAB toolbox.