Higher H\"older regularity for a subquadratic nonlocal parabolic equation

In this paper, we are concerned with the H\"older regularity for solutions of the nonlocal evolutionary equation ∂ₜ u+(-Δₚ)ˢ u = 0. Here, (-Δₚ)ˢ is the fractional p-Laplacian, $0<s<1$ and $1<p<2$. We establish H\"older regularity with explicit H\"older exponents. We also include the inhomogeneous equation with a bounded inhomogeneity. In some cases, the obtained H\"older exponents are almost sharp. Our results complement the previous results for the superquadratic case when p≥ 2.