A new class of nonlocal operators: the fractional logarithmic $p$-Laplacian and its properties

In this paper, we introduce and investigate the fractional logarithmic $p$-Laplacian $(-Δ)_{p}^{s+\log}$, defined as the first-order derivative with respect to the parameter $t$ of the fractional $p$-Laplacian $(-Δ)_{p}^{t}$ evaluated at $t=s$. We establish that this operator admits the following in