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

Researchers have introduced the Natural Transform Iterative Method (NTIM) as a novel and efficient approach for solving fractional differential equations. This technique integrates the Natural Transform with Daftardar-Jafari polynomials to generate approximate solutions without requiring discretization, linearization, or small parameters. NTIM has shown particular promise for fractional partial differential equations due to its straightforward application and quick convergence.

When compared to established methods like HPM, ADM, and FHATM, NTIM offers enhanced accuracy and computational efficiency. The method's effectiveness has been confirmed through numerical and graphical analyses against exact solutions, suggesting its suitability for a wider range of nonlinear fractional systems.

This development offers a more accurate and efficient analytical tool for tackling complex fractional differential equations, potentially leading to advancements in fields like thermal engineering where such models are crucial.