Numerical approximations of groundwater flow problem using fractional variational iteration method with fractional derivative of singular and nonsingular kernels

Abstract

This study aims to present the numerical approximations of groundwater flow problem, namely the time-fractional Boussinesq equation using the fractional variational iteration method. Fractional derivatives in time variable are taken in Caputo and Caputo–Fabrizio sense. This work compares the solutions of the time-fractional Boussinesq equation for the Caputo and Caputo–Fabrizio fractional operators. Graphical representation of the water table head’s behavior for different time values is shown.