Qualitative analysis of metformin drug administration in Caputo setting

Abstract

This study develops a mathematical link between pharmacokinetics and fractional calculus, emphasizing on metformin’s complex metabolic activities in diverse body areas. Our study proposes and evaluates a metformin kinetics model that incorporates homogenous dimensionality in the Caputo sense. To explore the uniqueness and existence of solutions, we adopt the Banach and Schauder fixed point theorems. The study includes equilibrium points, asymptotic stability in respect to certain parameters, and Lyapunov stable solutions. In addition, we investigate Ulam-type stability for the generalized model. The research finishes with a thorough theoretical analysis based on the generalized Adam–Bashforth–Moulton (A-B-M) technique, laying the groundwork for future empirical validation.

Keywords

• Pharmacokinetics
• Caputo derivative
• Stability analysis
• Fixed point theory
• Numerical simulation