The Fractional Helmholtz Equation models wave propagation in complex, attenuating media, or media with nonlocal properties that cannot be accurately represented by the classical Helmholtz equation. In this talk, I will show recent results on the well-posedness of the scattering problem for the Fractional Helmholtz Equation in the whole space, and discuss the recovery of the support of an inhomogeneity. Solving this inverse problem requires the introduction of a new set of special frequencies, known as transmission eigenvalues, of which we show the existence and discreteness. The recovery of the support of the inhomogeneity is then established, provided the frequency is not one of those transmission eigenvalues for the fractional Helmholtz problem.
