New groundwater flow equation with its exact solution

Abstract

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 was the well-known method of separation of variables. The problem with this method is the introduction of the eigenvalue that does not have physical meaning. The second method was achieved using novel integral equation called Atangana-transform, and this method yields an exact solution. An alternative method based on the modified Boltzmann transformation also yields the exact solution. Some numerical simulations were done to express the efficiency of the model. (C) 2016 Sharif University of Technology. All rights reserved.