Anomalous diffusion modeling by fractal and fractional derivatives

Authors:
Wen Chen;Hongguang Sun;Xiaodi Zhang;Dean Korošak
Affiliations:
Institute of Soft matter Mechanics, Department of Engineering Mechanics, College of Civil Engineering, Hohai University, No. 1 Xikang Road, Nanjing, Jiangsu 210098, PR China;Institute of Soft matter Mechanics, Department of Engineering Mechanics, College of Civil Engineering, Hohai University, No. 1 Xikang Road, Nanjing, Jiangsu 210098, PR China;Institute of Soft matter Mechanics, Department of Engineering Mechanics, College of Civil Engineering, Hohai University, No. 1 Xikang Road, Nanjing, Jiangsu 210098, PR China;University of Maribor, Smetanova ulica 17, SI-2000 Maribor, Slovenia
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper makes an attempt to develop a fractal derivative model of anomalous diffusion. We also derive the fundamental solution of the fractal derivative equation for anomalous diffusion, which characterizes a clear power law. This new model is compared with the corresponding fractional derivative model in terms of computational efficiency, diffusion velocity, and heavy tail property. The merits and distinctions of these two models of anomalous diffusion are then summarized.