  In this paper we study the fractional p(., .)-Laplacian and we introduce the
corresponding nonlocal conormal derivative for this operator. We prove basic
properties of the corresponding function space and we establish a nonlocal
version of the divergence theorem for such operators. In the second part of
this paper, we prove the existence of weak solutions of corresponding p(.,
.)-Robin boundary problems with sign-changing potentials by applying
variational tools.
