Dynamical Analysis of Time Fractional Radial Groundwater Flow Equation

In this study, a time-fractional extension of the classical Theis problem with an exponential source term is investigated in a confined aquifer. The governing equation is modeled using two different fractional derivatives—the Caputo and Atangana–Baleanu–Caputo (ABC) operators—to account for memory effects in groundwater flow. The Fractional Reduced Differential Transform Method (FRDTM) is applied to obtain approximate series solutions up to the fifth order. The impact of the fractional order α, the nature of the fractional kernel and the localized source term on the hydraulic head are explored at different radial positions. The comparative analysis between the Caputo and Atangana–Baleanu–Caputo (ABC) models reveals how memory effects and operator choice significantly influence the hydraulic head response, offering insights into selecting suitable models for aquifers with varying recharge characteristics.