New predefined-time stability theorem and synchronization of fractional-order memristive delayed BAM neural networks

This study introduces a novel theorem focusing on predefined-time stability within fractional-order systems and applies it to the domain of predefined-time synchronization in fractional-order memristive delayed bidirectional associative memory neural networks . Leveraging the inherent characteristics of fractional-order calculus and the fractional-order comparison principle, this theorem is showcased. Unlike existing predefined-time stability theorems that rely on integer-order counterparts, our theorem adopts the fractional-order framework. By utilizing this theorem as a foundation, efficient controllers are developed to achieve predefined-time synchronization. The theoretical outcomes are verified through the examination of two numerical examples, affirming the robustness and applicability of our approach. • A novel theorem on predefined-time stability in fractional-order systems is proposed, providing a more generalized formulation. • Predefined-time stability exhibits convergence time independent of initial values, enabling the design of controller parameters. • Sufficient conditions for guaranteeing predefined-time synchronization are obtained.