New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations

Abstract

The objective of this paper is to compute the new modified method of variational iteration and the Laplace Adomian decomposition method for the solution of nonlinear fractional partial differential equations. We execute a comparatively newfangled analytical mechanism that is denoted by the modified Laplace variational iteration method (MLVIM) and Laplace Adomian decomposition method (LADM). The effect of the numerical results indicates that the double approximation is handy to execute and reliable when applied. It is shown that numerical solutions are gained in the form of approximately series which are facilely computable.

Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

“…In this section, we recall some basic definitions on conformable Laplace transform and some results which will be used later on. We refer the reader to some related research studies in [4,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Also, we define conformable triple Laplace transform, which is defined in equation ( 6).…”

“…Finally, it is also a remarkable fact that there are a large number of studies in the theory and application of fractional differential equations based on this new definition of derivative, which have been developed in a short time. We refer to [4,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]] that many researchers have been worked on different analogues methods to solve partial fractional differential in conformable sense. Numerical and analytical techniques for solving conformable partial differential equations and conformable initial boundary value problems have been investigated in [36,37], respectively.…”

“…In addition, the conformable formulations of the coupled nonlinear Schrodinger equations [30] and Fokas-Lenells equation [35] were studied to obtain travelling wave solutions and optical solutions, respectively. e triple Laplace Adomian decomposition method and modified variational iteration Laplace transform method were studied in [27,28], respectively. Similarly, a combined method of both of the Laplace transform and resolvent kernel methods was introduced in [31].…”

Artificial neural networks: a practical review of applications involving fractional calculus

“…The interest in applying and solving fractional differential equations (FDEs) has increased in the last decades. Methods such as Laplace/Sumudu perturbation [62,67,68,98,114,122,123], Adomian decomposition [46,124,125], homotopy perturbation [126] or decomposition have been used to reach this objective. However, these methods are faced with the convergency, the stability, ability to handle strong non-linearities [127] even the presence of a persistent memory [128].…”

A Semi-Analytical Method to Investigate Fractional-Order Gas Dynamics Equations by Shehu Transform

“…The current technique has been shown to solve nonlinear models efficiently, straightforwardly, and appropriately, with approximates quickly convergent to accurate results [33][34][35][36][37][38][39][40]. Recently, a technique mixture with the Laplace transform and VIM was suggested [41,42] and Wu introduced a method modified via fractional calculus and Laplace transforms [43]: the Laplace variational iteration method for investigating nonlinear partial differential equations [44] and the schemes of fractional partial differential equations [45].…”