Fractional kinetics of compartmental systems. First approach with use digraph-based method.

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 quasi-positive model determine all possible realisation based on one-dimensional digraph theory. The proposed method was discussed and illustrated in detail with some numerical examples.

Author: Konrad Markowski
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