Abstract
We considered in the paper a mathematical model used to replicate the conversion from confined to unconfined flow due to groundwater abstraction. We argued that the existing model, while very useful, however, does not capture the effect of the aquitard with fractures, as in such media there is a crossover behavior from stretched exponential to power law. We modified the model by replacing the exponential decay component with the generalized Mittag-Leffler function, which yields a model with nonlocal properties. To solve the system, we consider two different approaches, the first consists of discretizing the model directly using the forward Euler method, and the second consists of converting the model to an integral equation and deriving the solution by employing a polynomial interpolation approach. We presented using the Von Neumann stability approach for the confined part and both yield stability unconditionally. Some numerical simulations are performed.
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