Computational Study of a Meshless Approach for Multi-Term Time-Fractional Models in Drug Dispersion and Absorption in Biological Tissues (European Journal of Pure and Applied Mathematics, 2025)
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.
Keywords: Hybrid numerical method, Mobile-immobile solute transport model, Caputo derivative, Embedded Runge–Kutta method, Fibonacci and Lucas polynomials.