Fractional Newtonian gravity, based on the fractional generalization of Poisson’s equation for Newtonian gravity, is a novel approach to Galactic dynamics aimed at providing an alternative to the dark matter paradigm through a non-local modification of Newton’s theory. We provide an in-depth discussion of the gravitational potential for the Kuzmin disk within this new approach. Specifically, we derive an integral and a series representation for the potential, we verify its asymptotic behavior at large scales, and we provide illuminating plots of the resulting equipotential surfaces.

中文翻译：

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关于分数牛顿重力的Kuzmin模型

分数牛顿重力基于牛顿重力的泊松方程的分数泛化，是一种新的银河动力学方法，旨在通过牛顿理论的非局部修改为暗物质范式提供替代方案。我们在这种新方法中对Kuzmin圆盘的重力潜力进行了深入的讨论。具体来说，我们推导了该势的积分表示和级数表示，我们在大尺度上验证了其渐近行为，并提供了所得等势面的照明图。