In this project we focus on anomalous and fractional dynamics in polymer membranes, which should occur at finite observation times whenever a system has strong memory and/or a complex dynamical potential energy surface. We propose NSE experiments on diluted suspensions of polymersomes made of poly(butadiene-co-ethyleneoxide) (PBD-PEO) in deuterated water. The elastic properties of these membranes are well known by direct methods, which facilitates the interpretation of the relaxation rates of the fluctuation modes in terms of well-known membrane-supported dispersion equations. Different curvatures will be accessed by varying the thickness-to-radius structural ratio within the preparative range (for vesicle radius 20nm < R h/R > 0.075) which will change chain entangling, the level of lateral stress and finally the chain mobility.