Anomalous diffusion modeling by fractal and fractional derivatives

作者：Chen Wen; Sun Hongguang^*; Zhang Xiaodi; Korosak Dean

来源：Computers & Mathematics with Applications, 2010, 59(5): 1754-1758.

DOI：10.1016/j.camwa.2009.08.020

• Heavy tail
• Anomalous diffusion
• Fractal derivative
• Fractional derivative
• Power law

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.

• 出版日期2010-3
• 单位河海大学