Recently a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed J. G. Amar and M. Semaan, Phys. Rev. E 93, 062805 (2016) which takes into account the critical island-size i, island fractal dimension d(f), substrate dimension d, and diffusion exponent mu, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i = 1 with d = 2. Here we present the results of simulations carried out in 1D (corresponding to d = 1) of island nucleation and growth with anomalous diffusion which were carried out for both the case of superdiffusion (mu > 1) and subdiffusion (mu < 1). Excellent agreement is found with the general RE theory for both irreversible growth (i = 1) and reversible growth with i = 2 for all 0 <= mu <= 2. Published by AIP Publishing.
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