Fractional-Order Pharmacokinetic Model for Oral Drug Absorption: A Two-Compartment Analysis Using Caputo Derivative

الملخص

The dynamics of drug absorption and distribution in the human body exhibit complex behavior characterized by memory effects and non-local interactions that traditional integer-order pharmacokinetic models fail to capture adequately. This paper presents a fractional-order mathematical model for oral drug absorption using the Caputo fractional derivative framework. We develop a two-compartment system representing the gastrointestinal tract and blood plasma, governed by fractional differential equations of order α ∈ (0, 1]. The existence and uniqueness of solutions are established via the contraction mapping theorem. Stability analysis reveals the presence of a continuum of equilibria along P = 0, demonstrating Lyapunov stability with P(t) → 0 as t → ∞ in the Mittag-Leffler sense. Numerical simulations employing the Adams-Bashforth-Moulton predictor-corrector method are conducted for fractional orders α = 0.5, 0.6, 0.75, 0.85, 0.92, 0.98, 0.99, 0.999. Results demonstrate that the absorption rate increases monotonically with α, with higher fractional orders (α ≈ 1) yielding faster drug absorption profiles that converge to the classical integer-order solution. The fractional model offers improved predictive capability for anomalous diffusion processes in biological systems, with potential applications in personalized medicine and drug delivery optimization.