By assuming the existing of memory effects and long-range interactions in the hot and dense matter produced in high energy heavy ion collisions, the nonextensive statistics together with the relativistic hydrodynamics including phase transition is used to discuss the transverse momentum distributions of charged particles produced in heavy ion collisions. It is shown that the combined contributions from nonextensive statistics and hydrodynamics can give a good description to the experimental data in Au+Au collisions at sqrt(s_NN )= 200 GeV and in Pb+Pb collisions at sqrt(s_NN) )= 2.76 TeV for pi^(+ -) , K^(+ -) in the whole measured transverse momentum region, and for p(p-bar) in the region of p_T<= 2.0 GeV/c. This is different from our previous work, where, by using the conventional statistics plus hydrodynamics, the describable region is only limited in p_T<= 1.1 GeV/c.
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