Solution of Fractional Third-Order Dispersive Partial Differential Equations and Symmetric KdV via Sumudu–Generalized Laplace Transform Decomposition

Abstract

This research work introduces a novel method called the Sumudu–generalized Laplace transform decomposition method (SGLDM) for solving linear and nonlinear non-homogeneous dispersive Korteweg–de Vries (KdV)-type equations. The SGLDM combines the Sumudu–generalized Laplace transform with the Adomian decomposition method, providing a powerful approach to tackle complex equations. To validate the efficacy of the method, several model problems of dispersive KdV-type equations are solved, and the resulting approximate solutions are expressed in series form. The findings demonstrate that the SGLDM is a reliable and robust method for addressing significant physical problems in various applications. Finally, we conclude that this transform is a symmetry to other symmetric transforms.

A Note on the Application of the Double Sumudu–Generalized Laplace Decomposition Method and 1+1- and 2+1-Dimensional Time-Fractional Boussinesq Equations

“…The double Sumudu transformation method was utilized in several papers (see [21][22][23]). Recently, the authors of [24,25] used Sumudu-generalized Laplace transform decomposition to solve fractional third-order dispersive partial differential equations and the 2+1-Pseudoparabolic Equation. The solution of the fractional-order Boussinesq equation was obtained by employing the Laplace transform and the Atangana-Baleanu fractional derivative operator in [26].…”

Application of Double Sumudu-Generalized Laplace Decomposition Method for Solving 21-Pseudoparabolic Equation

“…Recently, the researchers in [23] studied the solution of fractional third-order dispersive partial differential equations and symmetric KdV by utilizing Sumudu-generalized Laplace transform decomposition.…”