  I provide a derivation of some characteristic effects of Milgrom's modified
Newtonian dynamics (MOND) from a fractional version of Newton's theory based on
the fractional Poisson equation. I employ the properties of the fractional
Laplacian to investigate the features of the fundamental solution of the
proposed model. The key difference between MOND and the fractional theory
introduced here is that the latter is an inherently linear theory, featuring a
characteristic length scale $\ell$, whilst the former is ultimately nonlinear
in nature and it is characterized by an acceleration scale $a_0$. Taking
advantage of the Tully-Fisher relation, as the fractional order $s$ approaches
$3/2$, I then connect the length scale $\ell$, emerging from this modification
of Newton's gravity, with the critical acceleration $a_0$ of MOND. Finally,
implications for galaxy rotation curves of a variable-order version of the
model are discussed.
