# Uniqueness for weak solutions of parabolic equations with a fractional time derivative

## TL;DR

This paper establishes the uniqueness of weak solutions for a class of parabolic equations involving fractional time derivatives, specifically Marchaud or Caputo derivatives, in divergence form.

## Contribution

It introduces a novel approach to proving uniqueness for weak solutions of fractional parabolic equations by transferring the fractional derivative to the test function.

## Key findings

- Proved uniqueness of weak solutions for fractional parabolic equations.
- Extended the theory to divergence form equations with fractional derivatives.
- Provided a new method for handling fractional derivatives in weak formulations.

## Abstract

We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test function.