Meshless computation for partial differential equations of fractional order

Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, the numerical properties of partial differential equations of fractional order 21 are investigated by the use of a radial basis function interpolation scheme. The differential equations of fractional order are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. The accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order