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Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions

Author

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  • Morales-Delgado, V.F.
  • Taneco-Hernández, M.A.
  • Vargas-De-León, Cruz
  • Gómez-Aguilar, J.F.

Abstract

The aim of this paper is to provide a mathematical study of the amount of drug administered as a continuous intravenous infusion or oral dose. For this purpose, we consider fractional-order mammillary-type models describing the anomalous dynamics of exchange of concentrations between compartments at, constant input rates, power-law type, and in the form of oral doses at given (discrete) times. We have developed a general analysis strategy for these models, in which we have found closed-form analytical solutions written in terms of the multivariate Mittag-Leffler function. Numerical simulations have been performed using our formulas, with parameters from the literature.

Suggested Citation

  • Morales-Delgado, V.F. & Taneco-Hernández, M.A. & Vargas-De-León, Cruz & Gómez-Aguilar, J.F., 2023. "Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000656
    DOI: 10.1016/j.chaos.2023.113164
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    References listed on IDEAS

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    1. Ali Ahmadian & Norazak Senu & Farhad Larki & Soheil Salahshour & Mohamed Suleiman & Md. Shabiul Islam, 2013. "Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, December.
    2. Li, Zhiyuan & Liu, Yikan & Yamamoto, Masahiro, 2015. "Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 381-397.
    3. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Copot, Dana & Magin, Richard L. & De Keyser, Robin & Ionescu, Clara, 2017. "Data-driven modelling of drug tissue trapping using anomalous kinetics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 441-446.
    5. Vedat Suat Erturk & A.K. Alomari & Pushpendra Kumar & Marina Murillo-Arcila & Sundarapandian Vaidyanathan, 2022. "Analytic Solution for the Strongly Nonlinear Multi-Order Fractional Version of a BVP Occurring in Chemical Reactor Theory," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-9, June.
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