<p>Variable-order fractional calculus has emerged as a powerful modeling paradigm for systems whose memory and hereditary properties evolve dynamically over time. This paper presents a comprehensive study of variable-order fractional differential equations with variable coefficients and time-delay terms, where the fractional derivative is defined in the Caputo sense. The presence of both variable order and delay introduces non-trivial coupling effects that require careful analytical treatment. We rigorously establish Ulam–Hyers stability for the proposed system, confirming that solutions exhibit robust behavior under small perturbations in initial data and forcing terms. To obtain approximate solutions, we implement the Adams–Bashforth–Moulton predictor-corrector algorithm, a multi-step method well suited to fractional-order systems due to its favorable convergence and efficiency properties. Extensive computational simulations are conducted across a range of variable-order functions, illustrating the influence of order variation on solution trajectories and validating the theoretical stability findings. The results affirm the practical effectiveness of the proposed framework for analyzing complex variable-order fractional delay systems arising in physics, engineering, and biological modeling.</p>