Citation: Benetti, F.; Lapi, A.; Gandolfi, G.; Adil Butt, M.; Boumechta, Y.; Haridasu, B.S.; Baccigalupi, C. Dark Matter in Fractional Gravity III: Dwarf Galaxies Kinematics. Universe 2023, 9, 478. https://doi.org/10.3390/ universe9110478 Academic Editor: Mauro D’Onofrio Received: 16 October 2023 Revised: 2 November 2023 Accepted: 7 November 2023 Published: 8 November 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). universe Article Dark Matter in Fractional Gravity III: Dwarf Galaxies Kinematics Francesco Benetti 1,2, * , Andrea Lapi 1,2,3,4 , Giovanni Gandolfi 1,2,3 , Minahil Adil Butt 1,2,3 , Yacer Boumechta 1,2,3,5 , Balakrishna S. Haridasu 1,2,3 and Carlo Baccigalupi 1,2,3 1 Scuola Internazionale Superiore Studi Avanzati (SISSA), Physics Area, Via Bonomea 265, 34136 Trieste, Italy; lapi@sissa.it (A.L.); ggandolf@sissa.it (G.G.); mbutt@sissa.it (M.A.B.); yboumech@sissa.it (Y.B.); sandeep.haridasu@sissa.it (B.S.H.); bacci@sissa.it (C.B.) 2 Institute for Fundamental Physics of the Universe (IFPU), Via Beirut 2, 34014 Trieste, Italy 3 Istituto Nazionale Fisica Nucleare (INFN), Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy 4 Istituto di Radio-Astronomia (IRA-INAF), Via Gobetti 101, 40129 Bologna, Italy 5 ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy * Correspondence: fbenetti@sissa.it Abstract: Recently, we put forward a framework where the dark matter (DM) component within virialized halos is subject to a non-local interaction originated by fractional gravity (FG) effects. In previous works, we demonstrated that such a framework can substantially alleviate the small-scale issues of the standard ΛCDM paradigm, without altering the DM mass profile predicted by N-body simulations, and retaining its successes on large cosmological scales. In this paper, we investigate further, to probe FG via the high-quality data of individual dwarf galaxies, by exploiting the rotation velocity profiles inferred from stellar and gas kinematic measurements in eight dwarf irregulars, and the projected velocity dispersion profiles inferred from the observed dynamics of stellar tracers in seven dwarf spheroidals and in the ultra-diffuse galaxy DragonFly 44. We find that FG can reproduce extremely well the rotation and dispersion curves of the analyzed galaxies, performing in most instances significantly better than the standard Newtonian setup. Keywords: dark matter; gravity; galaxy kinematics 1. Introduction The standard ΛCDM cosmology envisages galaxies to be hosted in virialized halos of dark matter (DM), which largely dominate the total mass and, hence, mostly determine the overall gravitational potential well and the dynamical properties of the baryons [1,2]. Remarkably, the density distribution of such halos is predicted by N-body simulations to follow an approximately universal shape, well described by the classic Navarro–Frenk– White [3] profile ρ ∝ (r/r s ) −1 (1 + r/r s ) −2 , with r s being a characteristic scale radius where the logarithmic slope equals −2. Only a minor deviation from such a scale-invariant behavior is expected, which amounts to a relationship between r s and the total DM mass [4]. This is often expressed in terms of the concentration parameter c 200 ≡ R 200 /r s , with R 200 being the radius where the average DM density is 200 times that of a critical Universe ρ crit . In fact, recent zoom-in N-body simulations [5] have demonstrated that c 200 correlates very well with the mass M 200 ≡ (4π/3) 200 ρ crit R 3 200 over a remarkably extended range from M 200 ∼ 10 −5 M ⊙ to 10 15 M ⊙ . Although on large scales observational data undoubtedly confirms the above picture, in the realm of dwarf galaxies with total masses  10 11 M ⊙ the situation becomes more uncertain. The most relevant issue for the present context emerges from galaxy kinematics and/or gravitational lensing data, which seem to indicate a much flatter density profile in the inner regions (i.e., a core), with respect to the cuspy NFW behavior; this occurrence is often referred to as the cusp–core problem [6–9]. Universe 2023, 9, 478. https://doi.org/10.3390/universe9110478 https://www.mdpi.com/journal/universe