A Comparative Study of Two Novel Analytical Methods for Solving Time-Fractional Coupled Boussinesq-Burger Equation

In this paper, a comparative study between two different methods for solving nonlinear time- fractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. Furthermore, the VITM's capacity to surmount challenges arising from the identification of the overarching Lagrange multiplier stands as an augmenting facet, amplifying its advantage over the NTDM technique.