  In this work we study an inhomogeneous two-phase obstacle-type problem
associated to the $s$-fractional $p$-Laplacian. Besides the existence and
uniqueness of solutions, we study the convergence of the solutions when $s\to
1$ to the classical problem. We also study the continuous dependence with
respect to the level-set function $v$, yielding an existence result for a
two-phase obstacle-type problem with an implicit level-set function.
