  New solutions of relativistic wave equations are obtained in a unified manner
from generating functions of spinorial variables. The choice of generating
functions as Gaussians leads to representations in the form of generalized
fractional Fourier transforms. Wave functions satisfying the Dirac, Maxwell,
and Weyl equations are constructed by simple differentiations with respect to
spinorial arguments. In the simplest case, one obtains Maxwell and Dirac
hopfion solutions.
