用改进的分数阶Gompertz定律模拟生物系统
Modeling biological systems with an improved fractional Gompertz law
摘要：
本文的目的是通过一个函数关于另一个函数的分数阶导数的Caputo式定义来提供Gompertz定律的分数阶推广。特别是，我们观察到，提出的模型似乎是从其他尝试的分数修改这个模型，因为分数的性质是由一般的解决方案，即使在其渐近行为进行了很长一段时间，有很大的不同。然后，我们验证了所提出的模型，采用它作为一个参考系，模拟生物物理和环境工程，即：暗发酵，光发酵和微藻生物量的增长特别感兴趣的三个生物系统。
英文摘要：
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.
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