The measurement of azimuthal correlations of charged particles is presented for Pb-Pb collisions at s_NN=2.76 TeV and p-Pb collisions at s_NN=5.02 TeV with the ALICE detector at the CERN Large Hadron Collider. These correlations are measured for the second, third and fourth order flow vector in the pseudorapidity region |η| < 0.8 as a function of centrality and transverse momentum p_T using two observables, to search for evidence of p_T-dependent flow vector fluctuations. For Pb-Pb collisions at 2.76 TeV, the measurements indicate that p_T-dependent fluctuations are only present for the second order flow vector. Similar results have been found for p-Pb collisions at 5.02 TeV. These measurements are compared to hydrodynamic model calculations with event-by-event geometry fluctuations in the initial state to constrain the initial conditions and transport properties of the matter created in Pb–Pb and p–Pb collisions.[Figure not available: see fulltext.].