Abstract
This paper continues previous work on a possible alternative model of
gravity, based on fractional calculus applied to Newton's law of gravitation.
In particular, our Newtonian Fractional Gravity (NFG) is now applied to
axially-symmetric stellar structures, such as thin/thick disk galaxies
described by exponential, Kuzmin, or other similar mass distributions. As in
the case of spherically-symmetric structures, which was studied in previous
work on the subject, we examine a possible connection between NFG and Modified
Newtonian Dynamics (MOND), a leading alternative gravity model, which accounts
for the observed properties of galaxies and other astrophysical structures
without requiring the dark matter (DM) hypothesis. By relating the MOND
acceleration constant $a_0 1.2 10^ -10mþinspace
s^ -2$ to a natural scale length $l_0$ in NFG, namely $a_0 \approx
GM/l_0^2$ for a galaxy of mass $M$, and by using the empirical Radial
Acceleration Relation (RAR), we are able to explain the connection between the
observed radial acceleration $g_obs$ and the baryonic radial acceleration
$g_bar$ in terms of a variable local dimension $D$. As an example of this
methodology, we provide a detailed rotation curve fitting for the case of the
field dwarf spiral galaxy NGC 6503.
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