摘要：In this study, a dimensionally consistent governing equation oftransient unconfined groundwater flow in fractional time andmulti-fractional space is developed. First, a fractional continuity equationfor transient unconfined groundwater flow is developed in fractional timeand space. For the equation of groundwater motion within a multi-fractionalmultidimensional unconfined aquifer, a previously developed dimensionallyconsistent equation for water flux in unsaturated/saturated porous media iscombined with the Dupuit approximation to obtain an equation for groundwatermotion in multi-fractional space in unconfined aquifers. Combining thefractional continuity and groundwater motion equations, the fractionalgoverning equation of transient unconfined aquifer flow is then obtained.Finally, two numerical applications to unconfined aquifer groundwater floware presented to show the skills of the proposed fractional governingequation. As shown in one of the numerical applications, the newly developedgoverning equation can produce heavy-tailed recession behavior in unconfinedaquifer discharges.
