A numerical method is presented for solving third-kind linear Volterra integral equations with smooth (α = 0) and weakly singular (0 < α < 1) kernels. Using the operational matrix of fractional integration with Chelyshkov polynomials, the integral equation is transformed into a system of linear algebraic equations whose solution provides an accurate approximation. Residual error estimates are derived to assess the accuracy of the proposed method. Three numerical examples illustrate its efficiency, precision, and practical applicability.
