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

TL;DR

This paper establishes regularity and existence results for nonlinear parabolic equations involving fractional time derivatives with nonlocal Mittag-Leffler kernels, extending previous work to include viscosity solutions and nonlocal effects.

Contribution

It introduces new regularity and existence theorems for fractional parabolic problems with nonlocal Mittag-Leffler kernels, expanding the theoretical framework for such equations.

Findings

Proved Hölder regularity for solutions

Established existence of weak solutions

Extended results to viscosity solutions

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}})