<p>This paper investigates the problem of the numerical inversion of the generalized Erdélyi-Kober operator featuring a&#xa0;special function kernel. To address this problem, an original spline-operator method is proposed, integrating cubic spline interpolation with the analytical structure of the operator. Furthermore, theorems regarding the convergence and stability of the proposed numerical method are presented. Theoretical analysis demonstrates that the method achieves an <i>O</i>(<i>h</i>³) order of accuracy within the class of smooth functions. The influence of input data errors on the values of the inverse operator is investigated, and specific stability conditions are identified. The efficiency of the algorithm is validated through numerical experiments conducted in the Python programming environment using the model function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g(x) = x^{4.7}\)</EquationSource> </InlineEquation>. The results show full agreement with the theoretical estimates and demonstrate the high precision of the method in the approximate calculation of complex integral operators.</p>