Laplace New Iterative Method for solving time-fractional Sawada-Kotera and Lax KdV Equations

Abstract

This study investigates the use of the Laplace New Iterative Method (LNIM) to compute approximate solutions to the time-fractional Sawada–Kotera equation and the time-fractional Lax equation. The findings highlight that the method is straightforward to implement, especially within mathematical programming environments. Its performance is supported by the observed convergence of the approximate solutions toward the exact ones. In addition, the analysis shows that the solution behavior varies with the fractional order, capturing key features and properties of both equations.Moreover, the derived solutions align with the inherent structure of the two models, which supports the reliability and practicality of the Laplace New Iterative Method for this class of problems. The results also suggest that the approach is not restricted to these two equations and may be extended to other fractional sub-equations. Consequently, LNIM can be regarded as a significant numerical technique with potential applications across several scientific domains, including applied mathematics, physics, and engineering, reinforcing its relevance and motivating further work in this direction.