Modelling Fractional Behaviours Without Fractional Models

Abstract

This paper first warns about the confusion or rather the implicit link that exists in the literature between fractional behaviours (of physical, biological, thermal, etc. origin) and fractional models. The need in the field of dynamic systems modelling is for tools that can capture fractional behaviours that are ubiquitous. Fractional models are only one class of models among others that can capture fractional behaviours, but with associated drawbacks. Several other modelling tools are proposed in this paper, thus showing that a distinction is needed between fractional behaviours and fractional models.