The Clifford analysis extends the theory of complex variable functions
to high-dimensional spaces, which mainly studies the properties of
functions defined on $R^n$ with values in Clifford algebra $\mathrm{Cl}_{0,n}$. More
precisely, the quaternion algebra $H$ is isomorphic to the Clifford
algebra $\mathrm{Cl}_{0,2}$. I will present the differential formulas and the
uncertainty principles of the quaternion fractional Fourier transform,
the Clifford-Fourier transform, and the fractional Clifford-Fourier
transform.