Advanced Mathematical Models & Applications

This study presents an extension of a novel iterative approach rooted in the DGJ method for solving nonlinear functional equations, specifically targeting time-fractional partial differential equations with higher-order spatial derivatives. The technique is systematically applied to prominent equations, including the Sawada-Kotera-Ito, Lax's Korteweg-de Vries, Kaup-Kupershmidt, and Caudrey-Dodd-Gibbon equations, with the fractional derivatives interpreted in the sense of Caputo. Series solutions are constructed for each equation and rigorously compared against their respective exact analytical solutions, highlighting the accuracy and effectiveness of the proposed strategy. Furthermore, comprehensive graphical simulations illustrate the evolution of wave structures across various time intervals, complemented by numerical results that substantiate the convergence and computational simplicity of the method. The findings underscore the proposed DGJ-based technique as an effective and efficient tool for the study of time-fractional nonlinear evolution equations with high-order spatial derivatives.