Modelling von Bertalanffy growth function of fish with fractals

The von Bertalanffy growth function has been widely used by hydrobiologists to study the lifetime pattern of somatic growth in fishes. Recently, the new ontogenetic growth model has been introduced as a special case of the von Bertalanffy equation based on allometric scaling which has also been of particular importance since it offers the basic tools for deriving allometric associations for fish growth rates and the timing of life history events. In this manuscript, we extend these models by introducing four different fractal growth models based on the concept of fractal calculus. From mathematics perspectives, these models extend and generalize both the traditional and the ontogenetic growth models to new time scales and offer a number of motivating features not found in the basic models and in agreement with observations. The best of these models, in our opinion, corresponds to the one which takes into account anisotropy in a reservoir. Additional points have been obtained and discussed accordingly.