Fractional differential models for anomalous diffusion

In this study, we investigate three kinds of fractional differential models (distributed-order model, variable-order model and random-order model) for characterization of anomalous diffusion. The characteristics, physical advantages and potential applications of each model are highlighted. The numerical simulations also validate our analytical and comparison results. Furthermore, a generalized distributed–variable-order model and a more generalized distributed–variable–random-order model are proposed to combine the advantages of distributed-order model, variable-order model and random-order model.