Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations

Background: solute transport in highly heterogeneous media and even neutron diffusion nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that concentration profiles exhibit anomalous non-Fickian growth rates so-called “heavy tails”. Methods: a nonlinear-coupled 3D hydro-mechanical model accounting for (FD) advection–dispersion (FAD) flux is described, Riesz derivative treated through Grünwald–Letnikow definition. Results: long-tailed contaminant distribution displayed due to variation flow velocity both time distance. Conclusions: finite difference approximation proposed solve problem 1D domains, subsequently, two scenarios considered numerical computations.