Newtonian fractional-dimension gravity and the external field effect

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