Fractional Klein–Gordon equation on AdS₂₊₁

We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent metric underlying manifold. As an example we consider on AdS$_{2+1}$, computing explicit kernel representation Laplace-Beltrami operator as well two-point propagator equation. Our results suggest that only exists if mass is small compared to inverse AdS radius, presumably because space expands faster distance flat same dimension. are expected be useful in particular for new applications AdS/CFT correspondence within statistical mechanics and quantum information.