  In this manuscript we deal with existence/uniqueness and regularity issues of
suitable weak solutions to nonlocal problems driven by fractional Laplace type
operators. Different from previous researches, in our approach we consider
gradient non-linearity sources with subcritical growth, as well as appropriated
measures as sources and boundary datum. We provide an in-depth discussion on
the notions of solutions involved together with existence/uniqueness results in
different regimes and for different boundary value problems. Finally, this work
extends previous ones by dealing with more general nonlocal operators, source
terms and boundary data.
