  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.
