  We consider and discuss some basic properties of the bicomplex analog of the
classical Bargmann space. The explicit expression of the integral operator
connecting the complex and bicomplex Bargmann spaces is also given. The
corresponding bicomplex Segal--Bargmann transform is introduced and studied as
well. Its explicit expression as well as the one of its inverse are then used
to introduce a class of two--parameter bicomplex Fourier transforms (bicomplex
fractional Fourier transform). This approach is convenient in exploring some
useful properties of this bicomplex fractional Fourier transform.
