Global asymptotic stability and S-asymptotic ω-periodicity of impulsive non-autonomous fractional-order neural networks

This paper is concerned with the globally S-asymptotic ω-periodicity of impulsive non-autonomous fractional-order (FO) neural networks (NNs). The definition of the piecewise S-asymptotic ω-periodicity of the considered system is given and a new Banach space is constructed. Based on the Banach mapping principle, several novel criteria for the existence and uniqueness of piecewise S-asymptotically ω-periodical solutions are obtained. Then by the FO differential and integral inequalities, we discuss the globally asymptotic stability and globally asymptotic periodicity of the probed FONN. Our methods and results are new. Finally, a numerical example is given to verify the validity of our findings.