In this manuscript, we establish an existence result for an infinite mixed system of nonlinear Volterra–Fredholm integral equations in the sequence space \(\ell _p\) . The analysis combines the Meir–Keeler fixed point theorem with the measure of noncompactness (MNC), under the general framework of fixed point theory. These tools allow us to address both the nonlinearity and the infinite-dimensional setting in a unified framework, thereby ensuring the existence of a solution to the proposed integral system. To further illustrate the theoretical findings, we construct an example of such a nonlinear mixed Volterra–Fredholm system and demonstrate how the main existence theorem applies to it. This example not only validates the assumptions of our theoretical framework, but also highlights it’s practical applicability. In the final part of the manuscript, we introduce an iterative method that combines the modified homotopy perturbation method (MHPM) and Adomian’s decomposition method (ADM) to approximate the solution of the integral system with high accuracy. A thorough convergence analysis confirms that the sequence generated by the proposed algorithm converges in the \(\ell _p\) -norm. Additionally, a stability analysis evaluates the solution’s sensitivity to perturbations in the initial data. The numerical results support the theoretical findings and demonstrate the efficiency and high accuracy of the proposed method.
