From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such processes across various scales has important application to research in materials science, finance, medicine, and energetics. Here we present a numerical study of anomalous diffusion of light through a semicrystalline polymer structure where transport is guided by random disorder and nonlocal interactions. The numerical technique examines diffusion properties in one-dimensional (1D) space via the spectrum of an Anderson-type Hamiltonian with a discrete fractional Laplacian operator (−Δ)^s, s∈(0,2) and a random distribution of disorder. The results show enhanced transport for s<1 (superdiffusion) and enhanced localization for s > 1 (subdiffusion) for most examined cases. An important finding of the present study is that transport can be enhanced at key spatial scales in the subdiffusive case, where all states are normally expected to be localized for a (1D) disordered system.