  The emergence of the Ultra-Diffuse Galaxies in recent years has posed a
severe challenge to the galaxy formation models as well as the Extended
Theories of Gravity. The existence of both dark matter lacking and dark matter
dominated systems within the same family of astrophysical objects indeed
requires the gravity models to be versatile enough to describe very different
gravitational regimes. In this work, we study a non-local extension of the
theory of General Relativity that has drawn increasing attention in recent
years due to its capability to account for the late time cosmic acceleration
without introducing any dark energy fluid. We leverage the kinematic data of
three Ultra-Diffuse Galaxies: NGC 1052-DF2 and NGC 1052-DF4, which are dark
matter lacking, and Dragonfly 44, which exhibits a highly dominant dark matter
component. Our analysis shows that the non-local corrections to the Newtonian
potential do not affect the kinematic predictions, hence no spoiling effects
emerge when the Non-local Gravity model serves as a dark energy model. We
additionally provide the minimum value that the characteristic non-local radii
can reach at these mass scales.
