In quantum Hall edge states and in other one-dimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. In this talk I will consider a ν = 2 quantum Hall system, whose edge physics is described in terms of two co-propagating chiral Luttinger Liquids. Coupling between the two edge modes is introduced via a quantum quench protocol [1, 2], while two Quantum point contacts (QPCs) are used to selectively drive the edge modes out of equilibrium one with respect to each other. In order to study the relaxation dynamics of the inner edge mode, we employ the method of non-equilibrium bosonization [3]. Non-equilibrium bosonization is a convenient framework to study strongly interacting, one dimensional systems far from equilibrium in an exact way. The core feature of this method is the relation between the observables of the theory and the functional determinants of full counting statistics. First, I will discuss the long time limit of the fractionalization noise, corresponding to well separated fractional pulses [4]. Even in this asymptotic case, the edge distribution function does not thermalize, but instead depends in a sensitive way on the interaction strength between the two edge modes. We compute shot noise and Fano factor from the asymptotic distribution function of the inner edge mode, and from comparison with a reference model of fractionalized excitations we obtain the value of the fractional charge measured in a recent experiment [5]. Lastly, I will present a recent extension of the formalism [6] that allows to study the full relaxation dynamics of the electron pulses. Indeed, if the original charge pulse has some spatial width due to injection with a given sourcedrain voltage, a finite time is needed until the separation between the fractionalized pulses is larger than their width. Mathematically, the evaluation of functional determinants of overlapping pulses requires a fully quantum mechanical treatment due to the energy/time uncertainty relation. Experimentally, this situation is realized when the distance between the two QPCs is shorter than the separation length of the pulses.