The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order $0.5$ subject to a given initial condition. We establish the existence of a unique solution expressed via a Mittag-Leffler-type function. The delta-asymptotic behavior of the solution is examined, and its convergence properties are rigorously analyzed. Numerical experiments are conducted to illustrate the qualitative features of the solution. Furthermore, a neural network-based approximation is employed to validate and compare with the analytical results, confirming the accuracy, stability, and sensitivity of the proposed method.