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It has recently been demonstrated A. Giusti, Phys. Rev. D 101, 124029 (2020) that characteristic traits of Milgrom's modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to be tested in relevant astrophysical scenarios. Here, we investigate its implications on Jeans gravitational instability and related phenomena. We examine scenarios involving classical matter confined by gravity and extend our analysis to the quantum domain, through a Schr\"odinger-Newton approach. We also derive a generalized Lane-Emden equation associated with fractional gravity. Through comparisons between the derived stability criteria and the observed stability of Bok globules, we establish constraints on the theory's parameters to align with observational data.
Kamel Ourabah (Sat,) studied this question.