On a hybrid class of p -Laplacian boundary value problems with modified Mittag-Leffler kernel: application to nonlinear and mixed pharmacokinetic models

This study investigates a class of hybrid fractional pantograph differential equations (HFPDEs) under the \(p\)-Laplacian operator \(LO\), employing the extended Mittag-Leffler kernel (\(MMLK\)). We establish the existence and uniqueness of solutions using Krasnoselskii and Banach fixed point theorems (FPTs), and further explore their stability properties. To bridge the gap between theory and practice, we develop a novel numerical method based on Lagrange's interpolation polynomial. The effectiveness of this method is demonstrated through its application to nonlinear and mixed pharmacokinetic models. A specific case is provided to confirm the validity of the theoretical results.