The integration of fractional-order phase rotation with measure-theoretic harmonic analysis yields the Fractional Fourier–Stieltjes Transform (FrFST). However, extending this transform to singular distributions, unbounded Radon measures, and non-smooth boundary submanifolds requires a rigorous dual-space formulation. In this paper, we establish the generalized framework for the Fractional Fourier–Stieltjes Integral Transform in Distribution Spaces. By embedding bounded Borel measures  and singular distribution spaces into the Schwartz dual space  and Gel'fand–Shilov ultra-distribution spaces , we define the distributional action of -dimensional fractional quadratic phase operators. We construct a family of fractional pseudo-differential inversion operators that regularize chirp-modulated singular distributions. We prove that these generalized inversion operators achieve weak-* convergence in measure spaces, topological isomorphism in distribution spaces, and strong norm convergence in scale-adapted negative-order Sobolev spaces  for .

Keywords: Generalized Fractional Fourier–Stieltjes transform, Schwartz distribution spaces, Tempered distributions, Fractional pseudo-differential operators, Gel'fand–Shilov spaces, Chirp-modulated dual pairing