Abstract: The present study deals with the generalized one-dimensional (1-D) advection fractal dispersion (AFD) equation. The numerical simulation is carried out to simulate the plume’s fate and transport phenomenon in a finite ...

Abstract: This study develops a homotopy analysis method (HAM) for analytically solving a one-dimensional time-fractional advection-dispersion equation (FADE). The HAM is a powerful method for solving nonlinear ordinary and partial ...

Abstract: According to the hydrodynamic dispersion theories, the dispersion parameter is proportional to a power

Abstract: Using the Laplace integral transform technique (LITT), an analytical solution to the advection–dispersion–reaction (ADR) equation for a semi-infinite homogeneous geological formation is derived, considering the effect of ...

Abstract: Fractional derivatives, owing to their nonlocal behavior, are well suited for modeling the fate of contaminants in a heterogeneous medium. This study develops the mathematical formulation and the solution of a one-dimensional ...

Abstract: Using the Hankel Transform Technique, an analytical solution is derived for two-dimensional solute transport in a homogeneous isotropic aquifer. The aquifer is subjected to time-dependent point source contamination. The ...

Abstract: An analytical solution for the space-time variation of contaminant concentration in one-dimensional uniform groundwater flow in a homogenous semi-infinite porous formation (e.g., aquifer) subjected to time-dependent source ...

Abstract: The space-time variation in contaminant concentration in unsteady flow in a homogeneous finite aquifer subjected to point source contamination is analytically derived under two conditions: (1) the flow velocity in the ...

Abstract: Saltwater intrusion in a coastal region is one of the major issues facing the agricultural, domestic, and industrial sectors. Groundwater withdrawal for an increasing population and agricultural and industrial demands are ...