In this paper, we introduce a family of O_-transformation based on kernels fusion of the fractional Fourier transform (abbreviated as FRFT) with angle Z. We point out this is a valid integral transform via establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the O_-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, and Beurling-H\"ormander's theorem.
Minh et al. (2025) studied this question.