<p>The fractional Helmholtz equation with a fractional Laplacian has been proposed recently to better describe underlying anomalous behavior in geophysical electromagnetics, which motivates development of efficient numerical methods for computing its solutions. We derive the geometrical optics approximations, in the form of WKBJ and Babich’s ansatz, to approximate its solutions in the high frequency regime. Under the asymptotic approximations, the phase and amplitude are proved to satisfy an eikonal equation and a transport equation, respectively. Well-established schemes for Hamilton–Jacobi type equations are then adopted to compute the phase and amplitude numerically such that they can be used to build the wave through the asymptotic approximations. Numerical experiments with point source conditions, as well as comparisons to finite difference methods, are performed to demonstrate the effectiveness of the asymptotic approximations.</p>