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We prove H\"older estimates for viscosity solutions of a class of possiblydegenerate and singular equations modelled by the fractional $p$-Laplaceequation $$ \text{PV}\int_{\mathbb{R}^n}\frac{|u(x)-u(x+y)|^{p-2}(u(x)-u(x+y))}{|y|^{n+sp}}\, dy =0,$$ where $s\in (0,1)$ and $p>2$ or $1/(1-s)<p<2$. Our results also apply forinhomogeneous equations with more general kernels, when $p$ and $s$ are allowedto vary with $x$, without any regularity assumption on $p$ and $s$. Thiscomplements and extends some of the recently obtained H\"older estimates forweak solutions.

H\"older estimates for viscosity solutions of equations of fractional $p$-Laplace type