Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel

Abstract

We prove H\"older regularity results for a class of nonlinear parabolic problem with fractional-time derivative with nonlocal and Mittag-Leffler nonsingular kernel. Existence of weak solutions via approximating solutions is proved. Moreover, the H\"{o}lder continuity of viscosity solutions is obtained. We get the similar results as those obtained by Allen (see {\url{https://arxiv.org/abs/1610.10073}})