Hölder gradient estimates for fractional $p$-caloric functions

We establish interior $C^{1,\alpha }$ regularity estimates, for some $\alpha >0$, for fractional $p$-caloric functions when $p$ is in the range $p\in (2,2\mathrm{/}(1-s))$. As a consequence, we deduce improved regularity in time, which yields interior continuous differentiability in time for $p\in [1\mathrm{/}(1-s),2\mathrm{/}(1-s))$.