A generalized approach to the development of high order fractional kinetics models

Abstract

This work presents an approach to developing high-order fractional kinetic models. Certain chemical and biological reactions exhibit atypical kinetics with non-local behavior, deviating from classical kinetic models. These deviations are associated with anomalous diffusion processes that do not follow the classical Fick’s law. To model that anomalous kinetics, fractional equations are frequently used; their implementation is not trivial, as an incorrect formulation may result in inconsistencies with mass conservation. Therefore, we propose a strategy in which nonlinear reaction rates are defined as functions of the fractional derivatives of the species, following a structure analogous to the law of mass action. This approach allows the development of models that are consistent with the mass balance. Two case studies illustrate this issue: a second-order reversible reaction and a heterogeneous catalytic reaction. Results show that the proposed models are consistent with mass conservation and can predict the non-local behavior of the reaction systems.