  The supersymmetric evolution of the fragmentation functions (or timelike
evolution) within N=1 $QCD$ is discussed and predictions for the fragmentation
functions of the theory (into final protons) are given. We use a backward
running of the supersymmetric DGLAP equations, using a method developed in
previous works. We start from the usual QCD parameterizations at low energy and
run the DGLAP back, up to an intermediate scale -assumed to be supersymmetric-
where we switch-on supersymmetry. From there on we assume the applicability of
an N=1 supersymmetric evolution (ESAP). We elaborate on possible application of
these results to High Energy Cosmic Rays near the GZK cutoff.
