Modeling biological systems with an improved fractional Gompertz law

Frunzo, Luigi; Garra, Roberto; Giusti, Andrea und Luongo, Vincenzo (2019): Modeling biological systems with an improved fractional Gompertz law. In: Communications in Nonlinear Science and Numerical Simulation, Bd. 74: S. 260-267

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. (C) 2019 Elsevier B.V. All rights reserved.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 1007-5704
• Sprache: Englisch