Revisiting the Fractional‐Order Neural Networks With Discrete Delay Through Fixed‐Point Approach

Source abstract

ABSTRACT The standard class of fractional‐order neural networks with a single discrete‐time delay is examined in this study. By using the contraction mapping principle and Krasnoselskii fixed point result, we establish novel sufficient conditions to ensure the existence, uniqueness, and uniform stability of solutions. Under Lipschitz‐continuous activation functions, we derive a contraction condition guaranteeing the uniqueness of the solution on a finite time interval. Under bounded activation functions, we prove the existence of at least one solution via Krasnoselskii's theorem. Furthermore, if the initial histories of the solutions are close enough, uniform stability of the delayed fractional‐order neural networks is established in defined time intervals. Finally, the theoretical results are illustrated through examples. The work extends and generalizes previous studies on fractional‐order neural networks by incorporating time delays, which are biologically and physically significant in neural signal transmission.