In this work, we propose a mathematical model to depict the conversion of groundwater flow from confined to unconfined aquifers. The conversion problem occurs due to the heavy pumping of confined aquifers over time, which later leads to the depletion of an aquifer system. The phenomenon is an interesting one, hence several models have been developed and used to capture the process. However, one can point out that the model has limitations of its own, as it cannot capture the effect of fractures that exist in the aquitard. Therefore, we suggest a mathematical model where the classical differential operator that is based on the rate of change is substituted by a non-conventional one including the differential operator that can represent processes following the power law to capture the memory effect. Moreover, we revise the properties of the aquitard to evaluate and capture the behaviors of flow during the process in a different aquitard setting. Numerical analysis was performed on the new mathematical models and numerical solutions were obtained, as well as simulations for various fractional order values.

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