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 use the obtained solutions to construct observables that allow us to see different behaviour of quark and gluon initiated final-state radiation, i.e. the average transverse momentum $langle |k|rangle$ and energy contained in a cone. 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.
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