New Finite-Time and Global Mittag-Leffler Stability Criteria for Fractional-Order BAM Neural Networks with S-Type Distributed Delays

This paper investigates the stability analysis of a class of fractional-order bidirectional associative memory neural networks (FOBAMNNs) with S-type distributed delays, which incorporating both discrete and distributed delays through a Lebesgue-Stieltjes integral. Leveraging the properties of Riemann-Liouville fractional-order derivatives and integrals, along with the additivity of integration intervals and initial conditions, we transform fractional-order integrals of the state function involving S-type distributed delays into equivalent integrals without such delays. Utilizing the theory of contractive mapping and the Bellman-Gronwall inequality, the finite-time stability (FTS) and global Mittag-Leffler stability (GLMS) criteria are established when certain conditions were satisfied. Moreover, the two distinct types of stability, FTS and GMLS, in FOBAMNNs are governed by appropriate parameters, complementing each other and laying a new foundation for advancing research and practical applications in neural networks. Furthermore, the validity and practical applicability of the theoretical results are demonstrated through two illustrative numerical simulation examples.