This paper investigates the existence and stability of a fractional-order labor dynamics model formulated using the fractional Nabla difference operator, specifically the Atangana-Baleanu fractional derivative in the Caputo sense. The model incorporates fractional dynamics to capture memory effects and the complex interactions associated with workforce layoffs. First, we present the mathematical formulation of the system and discuss its relevance to labor dynamics. Using the fixed-point theory, we establish the existence and uniqueness of solutions, demonstrating that the system is well posed. Furthermore, we examine the stability of the model in the Mittag-Leffler-Hyers-Ulam sense, providing insight into its long-term qualitative behavior. Numerical simulations support the theoretical findings and demonstrate that the fractional-order parameter significantly influences the system's dynamics. Overall, this study offers a more general and flexible framework for modeling layoff processes using fractional calculus.

This study employs specific and appropriate criteria to investigate the global stability of hybrid bidirectional associative memory (BAM) neural networks with time delays. We establish new and more general conditions for global asymptotic robust stability (GARS) in time-delayed BAM neural networks at the equilibrium point. This represents the primary objective and novelty of this paper. The derived conditions are independent of the system parameter delay in BAM neural networks. Finally, we provide numerical examples to illustrate the applicability and effectiveness of our conclusions with respect to network parameters.

In this paper, we investigate the global asymptotic stability of complex-valued neural networks (CVNNs) subject to time-varying delays and parameter uncertainties. We establish novel stability conditions that guarantee both the existence and uniqueness of equilibrium states, as well as the global convergence of the network trajectories. By constructing a suitable Lyapunov-Krasovskii functional, the approach inherently accounts for the stability of CVNNs subject to time-varying delays. Finally, numerical examples are presented to verify the theoretical findings, illustrating both the effectiveness and the practical applicability of the proposed approach.