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

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.Comment: Accepted version to appear in Contemporary Mathematics. Corrected inaccuracies regarding historical results in the introduction. Also changed the initial condition for the equation and fixed typo