A matrix-based spectral method for the numerical approximation of the fractional Laplacian and the fractional $p$-Laplacian of functions defined on ${\mathbb{R}}^n$

Loïc Constantin, Carlota M. Cuesta, Francisco de la Hoz

Given a function $u$ defined on ${\mathbb{R}}^n$, its fractional $p$-Laplacian is given by $$(-Δ)_p^su(\vec x)=C_1(n,s,p)\int_{\mathbb R^n}\frac{|u(\vec x)-u(\vec y)|^{p-2}(u(\vec x)…