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Fractional differential models for anomalous diffusion |
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| Authors: | HongGuang Sun Wen Chen Changpin Li |
| Institution: | a Institute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University No. 1 Xikang Road, Nanjing, Jiangsu 210098, China b Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 4160 Old Main Hill, Logan, UT 84322-4160, USA c Department of Mathematics, Shanghai University, Shanghai 200444, China |
| Abstract: | 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. |
| Keywords: | Variable-order model Random-order model Distributed-variable-order model Multiple power-law |
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