In this paper, we introduce a family of integral transforms, denoted by Oα, and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle α∈/πZ. We demonstrate that the Oα
Nearby in the stack
-transformation constitutes a well-defined integral operator by establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the
Oα
-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, Pitt's inequality, and Beurling-Hörmander's theorem.