# Fractal kinetics versus fractional derivative kinetics Source: [Fractal kinetics versus fractional derivative kinetics]() Collection index: [llms.txt]() Data updated: 2025-10-24T22:07:28.132Z Authors: Francois Brouersa, Tariq J. Al-Musawib Published: 2017-12-01T21:27:38.000Z ## Abstract This study presents a detailed comparison of the two most popular fractal theories used in the field of kinetics sorption of pollutants in porous materials: the Brouers-Sotolongo model family of kinetics based on the BurrXII statistical distribution and the fractional kinetics based on the Riemann-Liouville fractional derivative theory. Using the experimental kinetics data of several studies published recently, it can be concluded that, although these two models both yield very similar results, the Brouers-Sotolongo model is easier to use due to its simpler formal expression and because it enjoys all the properties of a well-known family of distribution functions. We use the opportunity of this study to comment on the information, in particular, the sorption strength, the half-life time, and the time dependent rate, which can be drawn from a complete analysis of measured kinetics using a fractal model. This is of importance to characterize and classify sorbent-sorbate couples for practical applications. Finally, a generalization form of the Brouers-Sotolongo equation is presented by introducing a time dependent fractal exponent. This improvement, which has a physical meaning, is necessary in some cases to obtain a good fit of the experimental data. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()