Modeling biological systems with an improved fractional Gompertz law
arXiv:1807.05937 · doi:10.1016/j.cnsns.2019.03.024
Abstract
The aim of this paper is to provide a fractional generalization of the Gompertz law via a Caputo-like definition of fractional derivative of a function with respect to another function. In particular, we observe that the model presented appears to be substantially different from the other attempt of fractional modifications of this model, since the fractional nature is carried along by the general solution even in its asymptotic behavior for long times. We then validate the presented model by employing it as a reference frame to model three biological systems of peculiar interest for biophysics and environmental engineering, namely: dark fermentation, photofermentation and microalgae biomass growth.
arXiv comment14 pages, 5 figures, matches published version in CNSNS
References in corpus (14)
- A Caputo fractional derivative of a function with respect to another function
- Fractional Calculus: Integral and Differential Equations of Fractional Order
- Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
- Numerical evaluation of two and three parameter Mittag-Leffler functions
- No Nonlocality. No Fractional Derivative
- A comment on some new definitions of fractional derivative
- Fractional kinetics emerging from ergodicity breaking in random media
- On a fractional linear birth--death process
- A dynamic viscoelastic analogy for fluid-filled elastic tubes
- A fractional generalization of the Poisson processes
- Scott-Blair models with time-varying viscosity
- Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process
- Short note on the emergence of fractional kinetics
- On the propagation of transient waves in a viscoelastic Bessel medium