  We consider an inverse problem of determining the coefficients of a
fractional $p\,$-Laplace equation in the exterior domain. Assuming suitable
local regularity of the coefficients in the exterior domain, we offer an
explicit reconstruction formula in the region where the exterior measurements
are performed. This formula is then used to establish a global uniqueness
result for real-analytic coefficents. In addition, we also derive a stability
estimate for the unique determination of the coefficients in the exterior
measurement set.
