QUALITATIVE ANALYSIS AND NUMERICAL SIMULATIONS OF THE CAPUTO FRACTIONAL POROUS MEDIUM EQUATION IN (n + 1)-DIMENSIONS

In order to provide a solid foundation for modeling heat and mass transfer in fractal porous media, this work investigates the [Formula: see text]-dimensional nonlinear Caputo fractional porous medium (CFPM) equation, which takes non-local interactions and memory effects into account. We are able to capture diffusion processes that classical models are unable to adequately describe by using fractional-order derivatives. We explore how changing the fractional order affects the diffusion dynamics numerically using the finite volume element method (FVEM), emphasizing the role of memory effects on the transport processes in porous media. Our results show that slower diffusion rates and more strong memory effects are introduced at lower fractional orders, which are important parameters in complex porous materials. Comprehensive 2D and 3D visuals illustrate the impact of fractional dynamics on the transport processes in these mediums.