  By considering synchrotron radiative process in the internal shock model and
assuming that all internal shocks are nearly equally energetic, we analyze the
gamma-ray burst (GRB) emission at different radii corresponding to different
observed times. We apply this model to GRB 050904 and find that our analytical
results can provide a natural explanation for the multi-band observations of
GRB 050904. This suggests that the X-ray flare emission and the optical
emission of this burst could have originated from internal shocks being due to
collisions among nearly-equally-energetic shells ejected from the central
engine. Thus GRB 050904 appears to be a burst with super-long central engine
activity.
