In the last decades artificial recharge has attracted the attention of many countries where groundwater has been depleted or as a means of enhancing aquifer recharge where natural recharge is being severely affected by climate change. In this work, mathematical models depicting the flow of water within a fractured aquifer with permeable and impermeable rock matrices were considered to depict the flow of water within an artificially recharged aquifer. Using two different types of differential operators, two models were suggested. A model based on the classical differentiation, which does not consider the heterogeneity of the geological formation. A model based on nonlocal differential operator, which is able to include into mathematical formulation the effect of long-range dependency expressing the memory. For the classical case, the Laplace transform operator was used to derive the exact solution. For the nonlocal case, new numerical methods including Adams-Bashforth and Atangana-Seda scheme were used to provide approximate solutions. For each numerical scheme stability and convergence analysis were presented with numerical simulation for different values of fractional order.