Anomalous diffusion and fractional diffusion equations
Abstract
In this work we investigate the anomalous diffusion equations, usually applied to describe the anomalous diffusion, which employ fractional derivatives for the time or the spatial variables. In particular, we obtain exact solutions by taking a generic initial condition into account and developing a perturbation theory to investigate complex situations. We also verify that the fractional derivatives, when applied to the time variable, lead us to a anomalous diffusion with second moment finite, i.e., <χ2> ∝ tα (0 < α < 1, and α > 1, corresponding to sub and superdifusive behavior, respectively). By way of contrast, the fractional derivative applied to the spatial variable results in a anomalous diffusion where the second moment is not finite. These equations generalize the usual diffusion equation in order to incorporate several situations. We also employ the continuous time random walking formalism to investigate the implications obtained by using fractional derivatives in the diffusion equationDownloads
Download data is not yet available.
Published
2008-03-27
How to Cite
Gonçalves, G., Lenzi, M. K., Moraes, L. de S., Lenzi, E. K., & Andrade, M. F. de. (2008). Anomalous diffusion and fractional diffusion equations. Acta Scientiarum. Technology, 27(2), 123-131. https://doi.org/10.4025/actascitechnol.v27i2.1476
Issue
Section
Chemical Engineering
DECLARATION OF ORIGINALITY AND COPYRIGHTS
I Declare that current article is original and has not been submitted for publication, in part or in whole, to any other national or international journal.
The copyrights belong exclusively to the authors. Published content is licensed under Creative Commons Attribution 3.0 (CC BY 3.0) guidelines, which allows sharing (copy and distribution of the material in any medium or format) and adaptation (remix, transform, and build upon the material) for any purpose, even commercially, under the terms of attribution.
Read this link for further information on how to use CC BY 3.0 properly.
0.8
2019CiteScore
36th percentile
Powered by
0.8
2019CiteScore
36th percentile
Powered by