New groundwater flow equation with its exact solution


1 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State 9300 Bloemfontein, South Africa

2 Department of Mathematics, Faculty of Sciences, University of Istanbul, 1293 Istanbul, Turkey


A new model of groundwater flowing within a confined aquifer was proposed using the concept of local derivative with fractional order. The derivative used in this model obeys all the properties of a local derivative and has a fractional order. The new groundwater flow equation was solved analytically via three different analytical methods. The first method is the well-known method of separation of variable. The problem with this method is the introduction of the Eigen-value that does not have physical meaning. The second method was achieved using novel integral equation called Atangana-transform and this method yields exact solution. An alternative method based on the modified Boltzmann transformation also yields to exact solution. Some numerical simulations were done to express the efficiency of the model