<p>In this study, we employ the modified natural transform decomposition method (MNTDM) based on cubic order convergence of Newton–Raphson method and the iterative Sumudu transform method (ISUTM) to investigate the approximate solution of the time fractional Kawahara and modified Kawahara equation in the Caputo&#xa0;sense. The modified Adomian decomposition method and the iterative approach are utilized to identify the nonlinear components of the equations. Both the method provides a sequence of functions which converges rapidly to the analytical solution of the problems. And the approximate analytical solution to the partial differential equation is obtained through the application of the natural transform, inverse natural transform, Sumudu transform, and inverse Sumudu transform techniques, all performed without differentiating in the time domain. The advantage of employing this approach lies in its ability to generate analytical series solutions for the target equations without the need for discretization, transformation, or any limiting assumptions. The effectiveness of the methods is illustrated through three numerical examples in each case with the error analysis and central processing unit (CPU) time and theoretical concepts also clarified through uniqueness, convergence and stability analysis and the physical interpretation is represented using two-dimensional and three-dimensional figures. The suggested methods are efficient and reliable as compared to others and well as behaved with exact result. Also both methods offer a significant resource for theoretical research as well as practical engineering applications.</p>