# Study on the Application of the Fractional Calculus in Pharmacokinetic Modeling

The application of fractional calculus (FC) in biomedicine is discussed in this paper. We present three different integer order pharmacokinetic models with two and three compartments that are commonly used in cancer therapy, and we solve them numerically and analytically to show the absorption, distribution, metabolism, and excretion (ADME) of drugs or nanoparticles (NPs) in various tissues. Because tumour cell interactions are systems with memory, the fractional order framework, rather than ordinary and delay differential equations, is a superior way to explain cancer processes. To discretize the model and produce the fractional order form to represent the fractal processes of drug transport in the body, the nonstandard finite difference analysis or NSFD approach following the Grunwald-Letinkov discretization can be used. Implementing a simple and efficient numerical approach to solve these fractional order models will be critical. In order to develop the numerical solution of fractional order two and tri-compartmental pharmacokinetic models for oral drug administration, numerical techniques based on the finite difference scheme were used. The fractional order model extends the capabilities of the integer order model into the extended domain of fractional calculus, as demonstrated in this work. Furthermore, fractional order modelling gives more power to control the dynamical behaviours of the (ADME) process in different tissues because the order of fractional derivative can be used as a new control parameter to extract a variety of governing classes on the nonlocal behaviours of a model; however, integer order modelling gives more power to control the dynamical behaviours of the (ADME) process in different tissues. Only the local and integer order domains are addressed by the order operator. In reality, for this sort of application, NSFD may be employed as an effective and simple way to implement, and it provides a handy framework for solving the proposed fractional order models.

Author(S) Details

Tahmineh Aziz
Florida State University, US.

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