This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi polynomial method (GPM). We have provided proof to demonstrate the existence of a unique solution to the second sort of NFrIE in Hilbert space. The proof of the stability of the error has been described and discussed. These criteria are proven given the spectrum characteristics of a linear selfadjoint operator. Numerous applications, unique conditions, and specific situations are developed. Additionally, numerical examples are constructed to illustrate the efficiency and applicability of the method. Maple 18 software is utilized for the computation of all the numerical outcomes.