Nearly all experimental observations of quasi-ballistic heat flow are interpreted using Fourier theory with modified thermal conductivity. Detailed Boltzmann transport equation (BTE) analysis , however, reveals that the quasi-ballistic motion of thermal energy in semiconductor alloys is no longer Brownian but instead exhibits Lévy dynamics with fractal dimension α < 2. Here, we present a framework that enables full 3D experimental analysis by retaining all essential physics of the quasi-ballistic BTE dynamics phenomenologically. A stochastic process with just two fitting parameters describes the transition from pure Lévy superdiffusion as short length and time scales to regular Fourier diffusion. The model provides accurate fits to time domain thermoreflectance raw experimental data over the full modulation frequency range without requiring any 'effective' thermal parameters and without any a priori knowledge of microscopic phonon scattering mechanisms. Identified α values for InGaAs and SiGe match ab initio BTE predictions within a few percent. Our results provide experimental evidence of fractal Lévy heat conduction in semiconductor alloys. The formalism additionally indicates that the transient temperature inside the material differs significantly from Fourier theory and can lead to improved thermal characterization of nanoscale devices and material interfaces.