In a recent paper of Optics Letter(Fan Hongyi and Lu Hailiang,Optics Letters 28(2003)680)the complex fractional Fourier transform(CFFRT)is introduced,which is different from the usual two-dimensional real fractional Fourier transforms. In the present work we illuminate its definition from the point of view of rotation of the complex form of Wigner distributions as well as from the view of optical propagation mechanism in graded-index medium. The newly constructed quantum mechanical entangled state representations are used to link CFFRT to the Wigner distributions.