A Nondivergence Parabolic Problem with a Fractional Time derivative

Abstract

We study a nonlocal nonlinear parabolic problem with a fractional time derivative. We prove a Krylov-Safonov type result; mainly, we prove Holder regularity of solutions. Our estimates remain uniform as the order of the fractional time derivative approaches 1.

Final version accepted for publication in Differential and Integral Equations