Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer

In this study, a numerical solution for degenerate space–time fractional advection–dispersion equations is proposed to simulate atmospheric dispersion in vertically inhomogeneous planetary boundary layers. The derivative exists Caputo sense. We establish the maximum principle and priori estimates solutions. Then, we construct positivity-preserving finite-difference scheme, using monotone discretization space L1 approximation on non-uniform mesh time derivative. use appropriate grading techniques time–space order overcome degeneration weak singularity of at initial time. computational results are demonstrated Gaussian model as well layers defined by height-dependent wind flow diffusitivity, especially Monin–Obukhov model.