The classical Fourier–Stieltjes transform maps bounded complex Borel measures into bounded continuous functions via flat monochromatic plane waves. However, it lacks the flexibility to analyze signals and measures with non-stationary, quadratic phase dynamics or time-frequency/space-momentum correlations. In this paper, we extend the Fourier–Stieltjes transform to the fractional domain by defining the Fractional Fourier–Stieltjes Transform (FrFST) of order  for arbitrary bounded Borel measures . By introducing a parameterized family of -dimensional quadratic phase chirp kernels, we establish the fundamental operational calculus of the FrFST. We construct a rigorous multidimensional inversion formula for the FrFST utilizing parameterized Gaussian-chirp regularizing operators. We prove that as the regularization parameter , the inverse fractional operator converges weakly to  on -dimensional hyper-rectangles with -null boundaries, and converges strongly in negative-order Sobolev spaces  for .

Keywords: Fractional Fourier transform, Fourier–Stieltjes transform, Bounded variation measures, Chirp modulation, Fractional domain harmonic analysis, Singular measure recovery