Pointwise fundamental theorem of L-fractional calculus beyond analytic functions

Determine whether the fundamental theorem of L-fractional calculus (and its Caputo counterpart) can be strengthened from holding almost everywhere to holding at every point for a class of functions larger than analytic or fractional-analytic functions.

Background

The paper proves pointwise versions of the fundamental theorem for analytic (or fractional-analytic) data, while for general absolutely continuous functions the identities hold almost everywhere. Extending pointwise validity to a broader class would clarify solution notions and rigor in fractional calculus.