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

Abstract

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 multi-dimensional 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, a numerical application to an unconfined aquifer groundwater flow problem is presented to show the skills of the proposed fractional governing equation.