Newtonian Fractional-Dimension Gravity and Galaxies without Dark Matter

We apply Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model, to some notable cases of galaxies with little or no dark matter. In the case of the ultra-diffuse galaxy AGC 114905, we show that NFDG methods can effectively reproduce the observed rotation curve, by using a variable fractional dimension $D\left (R\right )$ as was done for other galaxies in previous studies. For AGC 114905, we obtain a variable dimension in the range $D \approx 2.2 -3.2$, but our fixed $D =3$ curve can still fit all the experimental data within their error bars. This confirms other studies indicating that the dynamics of this galaxy can be described almost entirely by the baryonic mass distribution alone. However, our NFDG model explains the residual discrepancies without using any dark matter component. In the case of NGC 1052-DF2, we use an argument based on the NFDG extension of the virial theorem applied to the velocity dispersion of globular clusters showing that, in general, discrepancies between observed and predicted velocity dispersions can be attributed to an overall fractal dimension $D <3$ of the astrophysical structure considered and not to the presence of dark matter. For NGC 1052-DF2 we estimate $D \approx 2.9$, thus confirming that this galaxy almost follows standard Newtonian behavior. We also consider the case of the Bullet Cluster merger (1E0657-56), assumed to be one of the strongest proofs of dark matter existence. A simplified but effective NFDG model of the collision shows that the observed infall velocity of this merger can be explained by a fractional dimension of the system in the range $D \simeq 2.4 -2.5$, again without using any dark matter.