The higher order fractional Calderón problem for linear local operators: Uniqueness

We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by linear partial differential operator (PDO) of order smaller than Laplacian. show that one can uniquely recover coefficients PDO from Dirichlet-to-Neumann (DN) map associated to perturbed FSE. This is proved two classes coefficients: which belong certain spaces Sobolev multipliers and bounded derivatives. Our generalizes recent results zeroth first perturbations higher perturbations.