Fractional residual series for conformable time-fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations of seventh order

The purpose of the present work is to analyze and investigate the analytical solution of the seventh-order fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations under the conformable derivatives. Using the residual series expansion algorithm, the posed fractional models are studied analytically and numerically. Simultaneously, convergence analysis and error estimation are performed for the proposed technique. For this purpose, an advanced numerical algorithm is designed to handle the complexity of nonlinear fractional terms. Some experiments are provided to support theoretical analysis in a one-dimensional finite compact regime in light of the conformable sense. Eventually, numerical comparison is performed with other existing techniques along with some two- and three-dimensional representative graphs. Physical interpretation of the solution behaviors is discussed as well for various α values in an adequate time duration. Comparative results indicate the superiority and great flexibility of the presented method for fractional evolution systems arising in nonlinear wave propagation phenomena.