A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative

One of the big problems we encounter in groundwater modeling is to provide a correct model that can be used to describe the movement of water via a particular geological formation. In this work, in order to further enhance the model of groundwater flow in a leaky aquifer, we made use of a new derivative called the local variable order derivative. The derivative includes into mathematical formula the complexity of the leaky aquifer, which is for instance the variation of the aquifer, or the heterogeneity of the leaky aquifer. The modified equation was solved using the concept of iterative method. We presented in detail the stability and the uniqueness of the special solution.