This study reports the measurement of the anyonic exchange phase $ \theta_{a} $ in a monolayer graphene Fabry-Pérot interferometer at filling factor $ \nu = 1/3 $. The experiment involves observing interference patterns that are sensitive to the presence of localized anyons in the interferometer bulk. The phase shift $ \theta_{a} $ is determined by analyzing the interference pattern's dependence on the interferometer area $ A_{I} $, magnetic field $ B $, and the number of quasiparticles $ N_{qp} $ in the system. The results show that $ \theta_{a} $ is approximately $ 2\pi/3 $, consistent with previous experiments in GaAs quantum wells and theoretical expectations for Abelian anyons. The study also reveals that quasiparticle equilibration times can be as long as 20 minutes, which allows for the independent variation of $ A_{I} $ and $ N_{qp} $ to precisely determine the interferometer phase and monitor the entry and exit of individual anyons. The observed phase slips, which are sudden changes in the interference phase, are interpreted as the entry of a single anyon into the interferometer. The results suggest that the average 'topological charge' of a mesoscopic quantum Hall device can be held constant over hour-long timescales. The slow quasiparticle dynamics in the graphene interferometer enable the quantitative study of fractionalized phases at the single anyon level. The measurement of few-anyon dynamical processes via the response of the interferometric phase to both $ \theta_{a} $ and Coulomb effects provides new insights into states where inter-quasiparticle correlations are important, such as in the formation dynamics of anyonic Wigner crystal states and hierarchical fractional quantum Hall states. The study also highlights the importance of understanding the dynamics of charge-neutral excitations that encode fermion parity, which is crucial for the detection of non-Abelian statistics. The results suggest that unambiguous detection of non-Abelian statistics may be within reach due to the exceptionally long timescales for charge motion observed in this system.This study reports the measurement of the anyonic exchange phase $ \theta_{a} $ in a monolayer graphene Fabry-Pérot interferometer at filling factor $ \nu = 1/3 $. The experiment involves observing interference patterns that are sensitive to the presence of localized anyons in the interferometer bulk. The phase shift $ \theta_{a} $ is determined by analyzing the interference pattern's dependence on the interferometer area $ A_{I} $, magnetic field $ B $, and the number of quasiparticles $ N_{qp} $ in the system. The results show that $ \theta_{a} $ is approximately $ 2\pi/3 $, consistent with previous experiments in GaAs quantum wells and theoretical expectations for Abelian anyons. The study also reveals that quasiparticle equilibration times can be as long as 20 minutes, which allows for the independent variation of $ A_{I} $ and $ N_{qp} $ to precisely determine the interferometer phase and monitor the entry and exit of individual anyons. The observed phase slips, which are sudden changes in the interference phase, are interpreted as the entry of a single anyon into the interferometer. The results suggest that the average 'topological charge' of a mesoscopic quantum Hall device can be held constant over hour-long timescales. The slow quasiparticle dynamics in the graphene interferometer enable the quantitative study of fractionalized phases at the single anyon level. The measurement of few-anyon dynamical processes via the response of the interferometric phase to both $ \theta_{a} $ and Coulomb effects provides new insights into states where inter-quasiparticle correlations are important, such as in the formation dynamics of anyonic Wigner crystal states and hierarchical fractional quantum Hall states. The study also highlights the importance of understanding the dynamics of charge-neutral excitations that encode fermion parity, which is crucial for the detection of non-Abelian statistics. The results suggest that unambiguous detection of non-Abelian statistics may be within reach due to the exceptionally long timescales for charge motion observed in this system.