Two Types of Stability Criteria for Incommensurate Fractional-Order Inertial Delay BAM Neural Networks

This study explores the global Mittag-Leffler stability and finite time stability of incommensurate fractional-order inertial delay BAM neural networks. Initially, the system, characterized by high-order incommensurate fractional-order dynamics, is transformed into a low-order system through an appropriate variable substitution. Subsequently, sufficient conditions for the achievement of global Mittag-Leffler stability and finite time stability are derived. These conditions are based on the properties of the Riemann-Liouville fractional derivative and integral, and the relation of fractional integral inequalities to the Bellman-Gronwall inequality. The efficacy and accuracy of the proposed theoretical results are substantiated through two numerical simulations.