The stock market modeling requires a complete statistical description of the price and its dynamics. We analyze the intra-day Brazilian stock market price fluctuations (IBOVESPA), in the period 2002-2004, considering q-Gaussians distributions P(q) (x,t) derived from Tsallis non- extensive statistics. Such distributions are solutions of a non-linear Fokker-Planck equation (F.P.E.), allowing to model the anomalous diffusion found at high frequency price time series from statistical feedback mechanisms in the dynamics of price formation. Our results show that, when returns are measured over intervals less than 30 minutes, the empirical distributions are well fitted by q- Gaussians, with stationary non-extensive parameter q and exponential damped tails. From the time scale properties of the first moments of the empirical distributions, we analyze the consistency between the observed time evolution and the foreseen behavior within the non-linear F.P.E. and get the model parameters that characterize our high frequency market dynamics. The presence of time correlation slows down the convergence of the price return distributions to a Gaussian regime according to C.L.T., giving rise to a new q-Gaussian regime for very short time scales, with super diffusive behavior driven by the considered F.P.E. Our results show that this modeling provides an adequate description of the dynamics of the Brazilian stock market intra-day price fluctuations.