a boundary element method approach to fractional diffusion-reaction equations with caputo derivative: applications to mathematical biology

In this study, a boundary element method (bem) is developed for solving the time-fractional diffusion-reaction equation. the model describes anomalous transport behavior accompanied by a linear decay reaction. the numerical algorithm is implemented in matlab, providing an efficient and accessible framework for fractional analysis. numerical results for a two-dimensional strip domain show excellent agreement with the analytical solution, with a maximum relative error below 0.2%. the proposed method demonstrates high accuracy and stability for reaction parameter values in the range of 0 to approximately 0.1, where the internal and boundary errors remain negligible. however, for larger reaction parameters, the internal errors increase noticeably, indicating the sensitivity of the method to stronger reaction effects. the presented approach offers a reliable computational tool for modeling fractional diffusion-reaction phenomena and can be applied to biological processes such as drug absorption, molecular transport, and chemical reactions in complex tissues.