This paper addresses the initial value problem for nonlinear Riemann-Liouville nabla discrete fractional difference equations of order \(1< \theta < 2\) . By utilizing the intrinsic properties of the fractional difference operator, the problem is reformulated as an equivalent Volterra summation equation. The existence and uniqueness of solutions are rigorously established using Picard’s successive iteration method and Banach’s fixed-point theorem. Furthermore, key inequalities for linear fractional difference equations are derived, providing foundational tools for further analysis. To examine the qualitative behavior of solutions, Lyapunov’s direct method is employed to establish sufficient conditions for asymptotic stability. To illustrate the theoretical results, examples are provided, which validate the stability of discrete fractional equations and demonstrate the convergence of solutions using Newton’s iteration method.
