In the topic of differential equation theory, a fundamental focus is the analysis of the existence, uniqueness, and stability of solutions. These aspects are critical in ensuring that solutions not only exist but are also well-defined and behave predictably under small perturbations. In recent decades, much attention has been directed toward exploring these properties in constant fractional differential equations. However, the study of variable-order systems remains relatively underexplored. In this study, we investigate a type of multivariable-order neural network using the fractional variable-order Atangana–Baleanu–Caputo (ABC) operator. This operator is significant because it extends the traditional Caputo fractional derivative to accommodate variable orders, which can model more complex and realistic dynamical behaviors. To highlight the novel characteristics of the neural network model governed by this operator, we derive specific solutions and analyze their properties. This involves a detailed examination of how the variable-order nature impacts the dynamics and potential applications of the neural network. To establish the theoretical foundation for the existence and uniqueness of solutions, we employ Schauder’s and Banach’s fixed point theorems. Furthermore, we explore the Ulam-Hyers stability of the proposed system’s solutions. To substantiate our theoretical findings, we develop and present several numerical simulations. These simulations serve to illustrate the behavior of the neural network model under various conditions and confirm the analytical results obtained. By doing so, we provide a comprehensive validation of the theoretical framework and demonstrate the practical applicability of the proposed model.