Charged particle momentum distribution in jets in ALICE

Jets are defined in QCD as cascades of consecutive emission of partons from an initial hard scattering. The process of parton showering and subsequent hadronisation is broadly known as fragmentation. They can be studied via the momentum distribution of hadrons in jets. High energy nucleus-nucleus collisions allow us to study parton fragmentation within a QCD medium, and the properties of this medium via the modification of the jet structure. The ALICE experiment at CERN LHC is a general-purpose heavy ion experiment designed to study the physics of strongly interacting matter and the Quark-Gluon-Plasma, with excellent charged particle reconstuction and identification capabilities over a wide momentum range. We present measurements of fragmentation functions for jets reconstructed from charged particles in the ALICE central barrel. First results for proton-proton collisions are discussed and the status of the corresponding analysis for heavy ion collisions is presented. We give an outlook on identified particle fragmentation functions.