GRÜNWALD-LETNIKOV FINITE DIFFERENCE SOLUTIONS FOR FRACTIONAL DIFFUSION MODELS

Abstract

Fractional differential equations provide a robust framework for modeling anomalous diffusion phenomena in various scientific fields. This paper presents a numerical approach to solve the fractional diffusion equation using the Grünwald-Letnikov approximation. A finite difference scheme is developed, with detailed stability and convergence analyses. We investigate multiple scenarios, including variations in fractional order, boundary conditions, and diffusion coefficients, to assess their impact on model dynamics. Numerical results, supported by a solved example and comprehensive scenario analyses, demonstrate the method’s accuracy and applicability. The findings enhance the understanding of fractional diffusion models in real-world contexts.