A Fractional Structural Derivative Model for Ultra-Slow Diffusion

CHEN Wen; HEI Xin-dong; LIANG Ying-jie

doi:10.3879/j.issn.1000-0887.2016.06.005

Volume 37 Issue 6

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CHEN Wen, HEI Xin-dong, LIANG Ying-jie. A Fractional Structural Derivative Model for Ultra-Slow Diffusion[J]. Applied Mathematics and Mechanics, 2016, 37(6): 599-608. doi: 10.3879/j.issn.1000-0887.2016.06.005

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A Fractional Structural Derivative Model for Ultra-Slow Diffusion

doi: 10.3879/j.issn.1000-0887.2016.06.005

¹State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering(Hohai University), Nanjing 210098, P.R.China;²College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(11372097)

Received Date: 2016-01-25
Rev Recd Date: 2016-03-04
Publish Date: 2016-06-15

Abstract

Abstract

The ultra-slow diffusion is even more slow than the power-law sub-diffusion and is widely observed in a variety of natural and engineering fields. The ultra-slow diffusion cannot be well described with the traditional anomalous diffusion models. The Sinai’s law of diffusion depicts a special type of ultra-slow diffusion which is characterized by a logarithmic stochastic relationship. In this study, the Sinai diffusion was extended to a general ultra-slow diffusion. In addition, in the proposed model the initial parameters were introduced to remedy the perplexing issue that the Sinai diffusion was not feasible around the initial period of the ultra-slow diffusion. As a generalized fractional-order derivative, the concept of the fractional structural derivative was also presented to establish the partial differential equation governing the ultra-slow diffusion.
- ultra-slow diffusion,
- Sinai stochastic model,
- inverse Mittag-Leffler function,
- fractional structural derivative,
- diffusion equation

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References(14)

References

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