Fractional analysis of Benjamin-Bona-Mahony equation across natural transform iterative method: thermal engineering implementations

In this study, we apply the Natural Transform Iterative Method (NTIM), a relatively new and efficient analytical tool for solving fractional differential equations (FDEs). NTIM combines the Natural Transform and Daftardar-Jafari polynomials to construct approximate solutions without the need for discretization, small parameters, or linearization. This method is particularly effective for handling fractional partial differential equations due to its simplicity and rapid convergence. In comparison with other established techniques, such as the Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), and Fractional Homotopy Analysis Transform Method (FHATM). NTIM demonstrates improved accuracy and computational efficiency. The method is validated through numerical and graphical comparisons with exact solutions, showing its potential for broader applications in nonlinear fractional systems.