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In this paper, we are concerned with the H\"older regularity for solutions of the nonlocal evolutionary equation ₜ u+ (-ₚ) ˢ u = 0. Here, (-ₚ) 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.
Garain et al. (Thu,) studied this question.