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Discontinuity, Nonlinearity, and Complexity 15(2) (2026) 199--210 | DOI:10.5890/DNC.2026.06.005

Kavitha Velusamy$^1$, Deepa Ravi$^2$, Sripathy Budhi$^3$, Dumitru Baleanu$^4$, Mallika Arjunan Mani$^5$

$^1$ Division of Mathematics and Robotics Engineering, School of Sciences, Arts & Media, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India

$^2$ Department of Mathematics, Panimalar Engineering College, Chennai–600123, Tamil Nadu, India

$^3$ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore--632014, India

$^4$ Department of Computer Science and Mathematics, Labanese American University, Beirut, Lebanon

$^5$ Department of Mathematics, School of Arts, Science and Humanities, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India

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Abstract

This paper investigates the effect of temperature on drug distribution between the stomach and bloodstream compartments of the human body, incorporating the influence of time-dependent transfer and elimination rates. The study reveals that drug distribution behaviour is significantly influenced by variations in surrounding temperatures and the dynamic nature of transfer and elimination parameters. A theoretical analysis is performed to establish the existence, uniqueness, and stability of solutions for the proposed models using Caputo fractional derivatives. Numerical simulations are conducted using the predictor-corrector method to validate the theoretical findings and examine the impact of different fractional orders (\(\kappa\)) on drug kinetics. Graphical representations of the numerical results highlight the combined influence of memory effects, time-dependent parameters, and temperature variations on drug dynamics, providing valuable insights into the pharmacokinetics of drugs modeled in this work.

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