Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

Abstract

In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.