# Continuity of solutions to a nonlinear fractional diffusion equation

## TL;DR

This paper establishes space-time Hölder continuity estimates for weak solutions of a nonlinear fractional p-Laplacian diffusion equation, using iterative discrete differentiation techniques.

## Contribution

It provides explicit Hölder exponents for solutions to a fractional p-Laplacian parabolic equation, advancing regularity theory for nonlinear nonlocal PDEs.

## Key findings

- Space-time Hölder estimates with explicit exponents
- Regularity results for weak solutions of fractional p-Laplacian equations
- Application of Moser-type iteration techniques

## Abstract

We study a parabolic equation for the fractional $p-$Laplacian of order $s$, for $p\ge 2$ and $0<s<1$. We provide space-time H\"older estimates for weak solutions, with explicit exponents. The proofs are based on iterated discrete differentiation of the equation in the spirit of J. Moser.