Numerical Analysis of the Time-Fractional Boussinesq Equation in Gradient Unconfined Aquifers with the Mittag-Leffler Derivative

Abstract

In this study, two numerical methods—the variational iteration transform method (VITM) and the Adomian decomposition (ADM) method—were used to solve the second- and fourth-order fractional Boussinesq equations. Both methods are helpful in approximating non-linear problems effectively, easily, and accurately. The fractional Atangana–Baleanu operator and ZZ transform were utilized to derive solutions for the equation. Two examples are discussed to validate the methods and solutions. The results demonstrate that both the VITM and ADM methods are effective in obtaining accurate and reliable solutions for the time-fractional Boussinesq equation.