Fractionalized mathematical models for drug diffusion

Abstract

In this study, an effort is made to develop mathematical models that may be used to explain the distribution of drug administration in the human body after oral and intravenous administration of the drug. The diffusion process was utilized to create three models, applying Fick’s principle and the law of mass action. The Sumudu transform algorithm analyzes the rate of change of concentration in various compartments, such as blood and tissue medium. The general solution of drug concentration is demonstrated in the form of extended Mittag-Leffler function. The amount of drug that is contained in each compartment has been determined via the use of numerical parameters. The effect of the fractional parameter on the drug concentration is shown in graphical form. Using MAPLE software, graphs are created to highlight the change in drug concentration over time. The fractional model gives important and relevant inferences to infer new information about the medical field.