(untitled) (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.