  The line of sight velocity dispersion of the ultra-diffuse galaxies (UDGs)
NGC1052-DF2 and NGC1052-DF4 have been reasonably explained only with the
baryonic matter, without requiring any dark matter contribution. The comparable
ratio between the baryonic and halo mass also ascertain the above claim for the
two dark matter deficit galaxies. This paves the way for analyzing alternative
gravity theories such as the $f(R)$ gravity and the Renormalization Group
correction to General Relativity (RGGR). The analysis of the line of sight
velocity dispersion shows that the choice of $f(R)$ gravity models such as
Taylor expanded $f(R)$ about $R=0$ or a simple power law model of choice $R^n$
is consistent with the observational data. Similar statistical analysis is done
for the RGGR and is also found to be a viable explanation for the observed
velocity dispersion. We perform a global fit of the model parameters together
with both the UDGs. The coupling parameters of the theories are considered as
the global ones, and local variables such as the scale parameters are
considered to be dependent on the individual galaxy.
