Relation between fractional order models and diffusion in the body

Abstract

Robain.DeKeyser} @ UGent.be).Abstract: This paper presents the mathematical roots in fractional calculus that are present in the modeling of diffusion in the human body. Respiratory diffusion, as well as drug diffusion, are discussed and presented with their common mathematical framework. The links and discussion presented in this paper suggests that emerging tools from fractional calculus are natural solutions for modeling complex phenomena in biological tissue.

Fractional-Order Closed-Loop Model Reference Adaptive Control for Anesthesia

“…In reference [17], the authors present the relationship between the diffusion process and fractional-order models. Also, the introduction of fractional-order pharmacokinetic models are presented in references [15,16,18,19] which represent the experimental data in a more precise way, thanks to the t −α decay of the fractional operators, and with this, a new line of investigation was opened ion the area of drug delivery systems.…”

“…Consider the fractional-order system given by (17) that satisfies assumptions 1-6 and the closed-loop model reference given by (17) and the control law…”

Robust control for time‐fractional diffusion processes: application in temperature control of an alpha silicon carbide cutting tool

“…As some example, diffusion interfaces in the human body, e.g. respiratory diffusion and drug diffusion [38], and transmission lines [39] can be mentioned. In this paper, the control objective is to tune the FO-PI/PD controller [40]…”

An epidemiological MSEIR model described by the Caputo fractional derivative

“…We find in the literature different models described by fractional derivatives, like the SIR model [6,7,21,24,47,50,60,61], the SIR model with vaccination [17,36,58], the SIRC model [17], the SEIR model [23,51], the MSEIR model [8], etc. We also refer some applications to biomedical modelling [11,29,44,45,48].…”