  We expand our analysis of Newtonian Fractional-Dimension Gravity (NFDG), an
extension of the classical laws of Newtonian gravity to lower dimensional
spaces, including those with fractional (i.e., non-integer) dimension. We apply
our model to four rotationally supported galaxies (NGC 5033, NGC 6674, NGC
5055, NGC 1090), in addition to other three galaxies (NGC 7814, NGC 6503, NGC
3741) which were analyzed in previous studies. NFDG is able to fit the rotation
curves of all these galaxies without any dark matter component.
  We also investigate the possible violation of the strong equivalence
principle, in relation to the External Field Effect (EFE), i.e., the dependence
of the internal motion of a self-gravitating system under freefall on an
external gravitational field. This effect is not present in Newtonian or
Einstein gravity, but is predicted by some alternative theories of gravity. On
the contrary, we show that NFDG does not imply the EFE, at least for values of
the fractional dimension in the range $1 \leq D \leq 3$.
  Using improved NFDG numerical computations, we analyze the rotation curves of
the aforementioned galaxies and obtain perfect fits to the experimental data,
by using a fractional-dimension function $D\left (R\right )$ which
characterizes each individual galaxy. In the galactic sample studied here with
NFDG methods, we do not detect any significant differences between galaxies
that are supposed to show/not show the EFE according to other alternative
theories. A larger sample of galaxies will be needed to fully determine the
absence of any external field effect in NFDG.
