  We propose a system of evolution equations that describe in-medium
time-evolution of transverse-momentum-dependent quark and gluon fragmentation
functions. Furthermore, we solve this system of equations using Monte Carlo
methods.
  We then quantify the obtained solutions in terms of a few characteristic
features, namely the average transverse momentum $\langle |k|\rangle$ and
energy contained in a cone, which allow us to see different behaviour of quark
and gluon initiated final-state radiation. In particular, the later allows us
to conclude that in the gluon-initiated processes there is less energy in a
cone, so that the quark jet is more collimated.
