Modeling biological systems with an improved fractional Gompertz law

被引：47

作者：

Frunzo, Luigi ^{[1
]}

Garra, Roberto ^{[2
]}

Giusti, Andrea ^{[3
,4
,5
]}

Luongo, Vincenzo ^{[1
]}

机构：

[1] Univ Naples Federico II, Dept Math & Applicat, Via Cintia 1, I-80126 Naples, Italy

[2] Univ Rome, Dept Stat Sci, Sapienza, Ple Aldo Moro 5, Rome, Italy

[3] Univ Bologna, Dept Phys & Astron, Via Irnerio 46, Bologna, Italy

[4] INFN, Via Irnerio 46, Bologna, Italy

[5] Ludwig Maximilians Univ Munchen, Arnold Sommerfeld Ctr, Theresienstr 37, D-80333 Munich, Germany

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2019年 / 74卷

关键词：

Gompertz growth law; Fractional calculus; Mittag-Leffler functions; Fractional derivative of a function with respect to another function; POLY-BETA-HYDROXYBUTYRATE; DARK FERMENTATION; BIOHYDROGEN PRODUCTION; HYDROGEN; RESPECT;

D O I：

10.1016/j.cnsns.2019.03.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：260 / 267

页数：8

共 48 条

[1] Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications [J].