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

Mark Allen

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

Analysis of PDEs 2018-01-03 v2

Authors: Mark Allen

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.

Keywords

weak solutions parabolic equations fractional time derivative Marchaud derivative Caputo derivative divergence form uniqueness

Cite

@article{arxiv.1705.03959,
  title  = {Uniqueness for weak solutions of parabolic equations with a fractional time derivative},
  author = {Mark Allen},
  journal= {arXiv preprint arXiv:1705.03959},
  year   = {2018}
}

Comments

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 typos

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