Fractional Differential Phenomenological Modeling for Diffusion and Dissipation Behaviors of Complex Media

PANG Guo-fei; CHEN Wen; ZHANG Xiao-di; SUN Hong-guang

doi:10.3879/j.issn.1000-0887.2015.11.001

Volume 36 Issue 11

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PANG Guo-fei, CHEN Wen, ZHANG Xiao-di, SUN Hong-guang. Fractional Differential Phenomenological Modeling for Diffusion and Dissipation Behaviors of Complex Media[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1117-1134. doi: 10.3879/j.issn.1000-0887.2015.11.001

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Fractional Differential Phenomenological Modeling for Diffusion and Dissipation Behaviors of Complex Media

doi: 10.3879/j.issn.1000-0887.2015.11.001

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;³Siemens PLM Software, Shanghai 200050, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(11372097);The National Science Fund for Distinguished Young Scholars of China(11125208)

Received Date: 2015-08-26
Rev Recd Date: 2015-09-07
Publish Date: 2015-11-15

Abstract

Abstract

A complex medium is generally a multiphase mixture. Unlike the classical solid, liquid and gas, its mechanical behaviors exhibit anomalous features such as the memory and the path-dependence characteristics, which can hardly be well described with the classical mechanics models of integral-order derivatives. From the viewpoint of mathematical and physical modeling, the local limit definition of the integral-order derivative is not suitable to depict such non-local mechanical behaviors. The fractional derivative is essentially an integro-differential operator with underlying clear statistical physical explanation and can accurately describe the global correlation of complex mechanical behaviors. Since 1990s, the fractional derivative modeling for anomalous mechanical behaviors of complex media has attracted extensive attention due to its merits of fewer parameters with clear physical explanations. From the phenomenological modeling perspective, a review was made on the applications and developments of the fractional and fractal derivative models for the diffusion and energy dissipation behaviors of complex media.
- complex medium,
- fractional derivative,
- fractal derivative,
- diffusion,
- dissipation,
- mathematical and physical modeling

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References(92)

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