Fractional adsorption diffusion

Abstract

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 2010 : Primary 65-XX, 45-XX, 97-XX; Secondary 65D15, 45E10, 44A35, 97N50