Fractional kinetics of compartmental systems: first approach with use digraph-based method

Konrad Andrzej Markowski

doi:10.1117/12.2281028

7 August 2017 Fractional kinetics of compartmental systems: first approach with use digraph-based method

Konrad Andrzej Markowski

Proceedings Volume 10445, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017; 104452J (2017) https://doi.org/10.1117/12.2281028
Event: Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2017, 2017, Wilga, Poland

Abstract

In the last two decades, integral and differential calculus of a fractional order has become a subject of great interest in different areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned in 1695 by Leibniz and L'Hospital. The first definition of the fractional derivative was introduced by Liouville and Riemann at the end of the 19th century. Fractional calculus was found to be a very useful tool for modelling the behaviour of many materials and systems. In this paper fractional calculus was applied to pharmacokinetic compartmental model. For introduced model determine all possible quasi-positive realisation based on one-dimensional digraph theory. The proposed method was discussed and illustrated in detail with some numerical examples.

Citation Download Citation

Konrad Andrzej Markowski "Fractional kinetics of compartmental systems: first approach with use digraph-based method", Proc. SPIE 10445, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2017, 104452J (7 August 2017); https://doi.org/10.1117/12.2281028

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KEYWORDS

Matrices

Systems modeling

Calculus

Tissues

Electrical engineering

Modeling

Analytical research

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