Qualitative Analysis of Metformin Drug Administration in Caputo Setting

Abstract

The study of drug metabolism is significant to establish the drug pro-file. The pharmacokinetics of the drug determines the concentrationof the drug in enumerable parts of the human body. In this paper, we develop a relationship between such processes of Pharmacokinetics with mathematical formulations using the tools from fractional calculus. As per the literature, for treating a type-II diabetes mellitus, Metformin is being used extensively. The Metformin metabolism encom-passes a large variety of metabolic processes in different parts of thebody. In the present study, we formulate and analyze a model of the Metformin kinetics taking into account a homogenous dimensionalityin Caputo sense. The Banach and Schauder fixed point theorems are employed to explore the uniqueness and existence results. The equilibrium point, asymptotic stability for the given parameters, and Lyapunov stable solutions are also discussed. Further, the Ulam’s type stabilityis explored for generalized model. Finally, the Adam-Bashful-Mouton(A-B-M) method in generalized form is used to validate the conclusions.