Global asymptotical ωω-periodicity of a fractional-order non-autonomous neural networks

•The non-existence of ωω-periodic solutions for periodic or autonomous fractional-order neural networks (FNN).•Proof of the existence and uniqueness result of S-asymptotically ωω-periodic solutions of a non-autonomous FNN.•A new concept of global asymptotical ωω-periodicity for fractional differential equations.•Some sufficient conditions on global asymptotical ωω-periodicity of a non-autonomous FNN.

We study the global asymptotic ωω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ωω-periodic or autonomous fractional-order neural networks cannot generate exactly ωω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ωω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ωω-periodic external inputs, asymptotically converge to the same nonconstant ωω-periodic function that may be not a solution.