Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: an iterative framework for nonlinear wave dynamics

This paper addresses the solution of the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation using the Conformable Laplace Decomposition Method(CLDM). The CDGSK equation, afundamental model in wave dynamics andfluid mechanics, is explored for its applications in quantummechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractionalderivatives influence the physical characteristics of wave propagation in both optical and quantumsystems. The exact solutions obtained provide insight into soliton behavior, essential for under-standing wave-particle interactions in quantumfields and light-matter interactions in optics. Thefractional nature of the equation allows for more accurate modeling of non-integer order dynamicscommonly found in opticalfibers and quantum waveguides. The CLDM method proves to be highlyeffective, providing approximate solutions with minimal computational effort. Thesefindings offersignificant contributions to thefields of quantum mechanics and nonlinear optics, where thefractional CDGSK equation can be applied to solve complex wave equations with great accuracy.