Holder Regularity for Nondivergence nonlocal parabolic equations

TL;DR

This paper establishes Hölder continuity of viscosity solutions for nonlocal parabolic equations with generalized fractional time derivatives, extending regularity results to a broader class of nonlocal and fractional differential equations.

Contribution

It proves Hölder regularity for solutions to nonlocal parabolic equations with Marchaud or Caputo derivatives, including preliminary results for related nonlinear ODEs.

Findings

Viscosity solutions are Hölder continuous under the given conditions.

Regularity results extend to equations with generalized fractional derivatives.

Preliminary results for nonlinear ODEs involving fractional derivatives are established.

Abstract

This paper proves H\"older continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first shows that viscosity solutions to certain nonlinear ordinary differential equations involving the generalized fractional time derivative are H\"older continuous.