Abstract

Advection and dispersion are the movements of contaminants/solute particles along with flowing groundwater at the seepage velocity in porous media. The aim of this paper is to find concentration of contaminant in flowing groundwater using fractional advection dispersion equation with decay involving Hilfer derivative with respect to time. Time fractional advection-dispersion equation describe particle's motion with memory in time. The solution of time fractional advection dispersion equation with decay is obtained in terms of Mittag-Leffler function and Green function. The effect of the decay is to reduce mass and concentration of the solution, which is a function of time and space variable.

Keywords: Time fractional advection dispersion equation; decay rate coefficient; Fourier transform; Laplace transform; Hilfer derivative; Mittag-Leffler function.

MSC: 34A08, 26A33

Pages:  5$-$15     

Volume  71 ,  Issue  1-2 ,  2019