On the Finite-Time Boundedness and Finite-Time Stability of Caputo-Type Fractional Order Neural Networks with Time Delay and Uncertain Terms

Abstract

This study investigates the problem of finite-time boundedness of a class of neural networks of Caputo fractional order with time delay and uncertain terms. New sufficient conditions are established by constructing suitable Lyapunov functionals to ensure that the addressed fractional-order uncertain neural networks are finite-time stable. Criteria for finite-time boundedness of the considered fractional-order uncertain models are also achieved. The obtained results are based on a newly developed property of Caputo fractional derivatives, properties of Mittag–Leffler functions and Laplace transforms. In addition, examples are developed to manifest the usefulness of our theoretical results.

Keywords

• neural networks
• fractional order
• time delay
• uncertain parameters
• finite-time stability
• finite-time boundedness