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Fractional Calculus and Applied Analysis

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Fractional adsorption diffusion

Gerd Baumann
  • Mathematics Department, German University in Cairo, New Cairo City, Egypt
  • Department of Mathematical Physics, University of Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany
  • Email:
/ Frank Stenger
  • School of Computing, University of Utah, 3414 Merrill Engineering Bldg., Salt Lake City, UT, 84112, USA
  • Email:
Published Online: 2013-06-26 | DOI: https://doi.org/10.2478/s13540-013-0046-3


The aim of this article is to generalize the diffusion based adsorption model to a fractional diffusion and fractional adsorption model. The models are formulated as nonlinear fractional boundary value problems equivalent to a singular Hammerstein integral equation. The novelty is that not only the diffusion component of the model is fractionalized but also the adsorption part. The singular Hammerstein integral equation is solved by Sinc approximations. Specific numerical schemes are presented. Based on these solutions we are able to identify different regimes of adsorption diffusion processes controlled by fractional derivatives verified by experimental data. These regimes allow to classify experiments if examined with respect to their scaling behavior.

MSC: Primary 65-XX, 45-XX, 97-XX; Secondary 65D15, 45E10, 44A35, 97N50

Keywords: Sinc method; fractional calculus; approximation

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About the article

Published Online: 2013-06-26

Published in Print: 2013-09-01

Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0046-3. Export Citation

© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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