<p>In this paper, we use the Iterative Refinement Method (IRM), recently developed by the first author, to solve a challenging system of fractional Fredholm-Hammerstein integro-differential equations. We prove a convergence theorem that rigorously demonstrates the effectiveness of the IRM in approximating solutions to these equations. The theorem provides insight into the conditions under which the method converges, ensuring that the solutions not only exist but can also be effectively computed. To illustrate the practical applicability of our method, we present several numerical examples. These examples are carefully chosen to highlight the strengths of the IRM compared to traditional solution techniques. The numerical results confirm our theoretical results, showcasing the convergence rate and accuracy of our algorithm. This work contributes to the ongoing effort to refine computational methods for fractional calculus problems, supporting the potential of the IRM as a robust tool for researchers and practitioners facing similar mathematical challenges.</p>