A semi‐analytical approach for fractional order Boussinesq equation in a gradient unconfined aquifers

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 and the 2 n d ‐order in 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.