In this investigation, we propose a semi-analytical technique to solve the fractional order Boussinesq equation (BsEq) that pertains the groundwater level in a gradient unconfined aquifer having an impervious extremity. With the aid of Antagana-Baleanu fractional derivative operator and Laplace transform, several novel approximate-analytical solutions of the fourth-order time-fractional BsEq in R, Rn and the 2nd-order in R are derived. We analyze the most dominant ideology of differentiation, including the nonsingular kernel relying on the extended Mittag-Leffler type function to modify BsEq. Furthermore, we demonstrate the existence and uniqueness of the solution for the non-linear fractional BsEq. The present method is appealing and the simplistic methodology indicates that it could be straightforwardly protracted to solve various nonlinear fractional-order partial differential equations.
