Improved Soliton Solutions of Generalized Fifth Order Time-Fractional KdV Models: Laplace Transform with Homotopy Perturbation Algorithm

The main purpose of this research is to propose a new methodology to observe a class of time-fractional generalized fifth-order Korteweg-de Vries equations. Laplace transform along with a homotopy perturbation algorithm is utilized for the solution and analysis purpose in the current study. This extended technique provides improved and convergent series solutions through symbolic computation. The proposed methodology is applied to time-fractional Sawada-Kotera, Ito, Lax's, and Kaup-Kupershmidt models, which are induced from a generalized fifth-order KdV equation. For validity purposes, obtained and existing results at integral orders are compared. Convergence analysis was also performed by computing solutions and errors at different values in a fractional domain. Dynamic behavior of the fractional parameter is also studied graphically. Simulations affirm the dominance of the proposed algorithm in terms of accuracy and fewer computations as compared to other available schemes for fractional KdVs. Hence, the projected algorithm can be utilized for more advanced fractional models in physics and engineering.

Automated summary

This research proposes a new methodology to observe a class of time-fractional generalized fifth-order Korteweg-de Vries equations and applies it to several related models. The method provides improved and convergent series solutions through symbolic computation. The results show that this method outperforms other fractional KdV schemes in terms of accuracy and computational complexity.