ABSTRACT
Groundwater is recharged by rain water or spreading the water on the ground in vertical direction, and hence, the wetness of the soil increases. The obtained mathematical model has been solved using the Caputo, Caputo--Fabrizio and Atangana--Baleanu fractional derivative operators, respectively. The q-homotopy analysis method is applied to obtain the solutions of the equations and is affirmed by comparing the model results with those available in the literature. In this method, we have great freedom to choose the auxiliary parameter $h$, auxiliary function $H(\xi,T)$ and the initial guesses, and we can adjust and control the convergence region of solution series by choosing proper values for auxiliary parameter $h$, auxiliary function $H(\xi,T)$.
