  Bifractional displacement operators, are introduced by performing two
fractional Fourier transforms on displacement operators. They are shown to be
special cases of elements of the group G, that contains both displacements and
squeezing transformations. Acting with them on the vacuum we get various
classes of coherent states, which we call bifractional coherent states. They
are special classes of squeezed states which can be used for interpolation
between various quantities in phase space methods. Using them we introduce
bifractional Wigner functions A(?, ?; ??, ??), which are a two-dimensional
continuum of functions, and reduce to Wigner and Weyl functions in special
cases. We also introduce bifractional Q-functions, and bifractional
P-functions. The physical meaning of these quantities is discussed.
