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

System of evolution equations for quark and gluon jet quenching with broadening