Computational Study of a Meshless Approach for Multi-Term Time-Fractional Models in Drug Dispersion and Absorption in Biological Tissues

Authors

  • Imtiaz Ahmad Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, Malaysia.
  • Rashid Jan Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia.
  • Normy Norfiza Abdul Razak Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia.
  • Aziz Khan Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia.
  • Thabet Abdeljawad Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia.

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5684

Keywords:

Hybrid numerical method, Mobile-immobile solute transport model, Caputo derivative, Embedded Runge–Kutta method, Fibonacci and Lucas polynomials.

Abstract

This study presents a hybrid numerical approach for solving the multi-term time-fractional mobile-immobile diffusion equation. The proposed method combines a fractional Liouville-Caputo scheme for time derivatives with the embedded Runge–Kutta method (RK23) and employs a meshless technique using Fibonacci and Lucas polynomials for spatial derivatives. The accuracy and effectiveness of the approach are evaluated through numerical experiments using the $Max~error$ and $RMS$ error norms. This study highlights the advantages of meshless techniques, particularly their flexibility in higher-dimensional applications and ease of implementation. The numerical results obtained are validated against exact solutions, confirming the efficiency and accuracy of the proposed method.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Imtiaz Ahmad, Rashid Jan, Normy Norfiza Abdul Razak, Aziz Khan, Thabet Abdeljawad

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How to Cite

Computational Study of a Meshless Approach for Multi-Term Time-Fractional Models in Drug Dispersion and Absorption in Biological Tissues. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5684. https://doi.org/10.29020/nybg.ejpam.v18i2.5684