A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method

Abstract

In this article, we applied a new technique for solving the time-fractional coupled Korteweg-de Vries (KdV) equation. This method is a combination of the natural transform method with the Adomian decomposition method called the natural decomposition method (NDM). The solutions have been made in a convergent series form. To demonstrate the performances of the technique, two examples are provided.

Analytical Method for Solving Inviscid Burger Equation

“…Khan derived [20] an integral transform for the N-transform. Belgacem and Silambarasan [5,6] discovered the name natural transform and also applied the NDM method to solved many non-linear differential equations like that, Maxwells equation [7], nonlinear PDEs [25], fractional telegraph equation [9], Time-Fractional coupled Korteweg-de vries equation [10], Sine-Gordon equation [26], nonlinear fractional-order differential equations [16]. There are many other similar transform and decomposition methods which are used to solved differential and integral equations such as Natural Daftardar-Jafari Method (NDJM) [18], Gupta integral transform [15], Adomain Decomposition Method [24], Laplace Decomposition Method [2], and Differential Transform Method [1].…”

Modified conformable double Laplace–Sumudu approach with applications

“…Unfortunately, this integral transformation cannot directly handle nonlinear equations, unlike other integral transformations. Because of this, mathematicians have developed new techniques that incorporate integral transformations with numerical methods like the decomposition method, the perturbation method, the iteration variation method, and others [ [49] , [50] , [51] , [52] , [53] , [54] , [55] , [56] , [57] , [58] , [59] ].…”

The Analysis of Fractional-Order Kersten–Krasil Shchik Coupled KdV System, via a New Integral Transform

“…Numerous variations of this Kersten-Krasil'shchik coupled KdV-mKdV nonlinear system have been introduced by many researchers [13][14][15][16]. Many researchers applied different analytical and numerical methods to investigate KdV equations, such as the homotopy analysis method [17], expansion method [18], shifted Legendre polynomials [19], and natural decomposition method [20].…”