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.

Modeling biological systems with an improved fractional Gompertz law / Frunzo, L.; Garra, R.; Giusti, A.; Luongo, V.. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 74:(2019), pp. 260-267. [10.1016/j.cnsns.2019.03.024]

Modeling biological systems with an improved fractional Gompertz law

Garra R.;Luongo V.
2019

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.
2019
Fractional calculus; Fractional derivative of a function with respect to another function; Gompertz growth law; Mittag–Leffler functions
01 Pubblicazione su rivista::01a Articolo in rivista
Modeling biological systems with an improved fractional Gompertz law / Frunzo, L.; Garra, R.; Giusti, A.; Luongo, V.. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 74:(2019), pp. 260-267. [10.1016/j.cnsns.2019.03.024]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1554554
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