THERMAL SCIENCE

International Scientific Journal

Xiaoting Liu

,

HongGuang Sun

,

Mihailo P. Lazarević

,

Zhuojia Fu

A VARIABLE-ORDER FRACTAL DERIVATIVE MODEL FOR ANOMALOUS DIFFUSION

ABSTRACT
This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
KEYWORDS
anomalous diffusion, variable-order fractal derivative, stretched Gaussian distribution, porosity-gradient
PAPER SUBMITTED: 2016-04-15
PAPER REVISED: 2016-05-10
PAPER ACCEPTED: 2016-06-15
PUBLISHED ONLINE: 2016-10-01
DOI REFERENCE: https://doi.org/10.2298/TSCI160415244L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 1, PAGES [51 - 59]
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A variable-order fractal derivative model for anomalous diffusion

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