Anomalous Diffusion with Step-Function Injection in a Radial Geometry

An generalized advection dispersion model with time-fractional derivative is developed for analyzing underground injection of wastes. The governing equations for a cylindrically symmetrical system are cast in nondimensional form and then transformed and solved in Laplace space. With the help of Crump algorithm, the Laplace space solution is inverted. The effect of fractional derivative parameter to the particle movement process is discussed numerically, and it is pointed out that the role of fractional derivative parameter is to slow the particle motion when $0<\beta<1$.