New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma‐Tasso‐Olver Equations

Khan, Mohammad Jibran; Nawaz, Rashid; Farid, Samreen; Iqbal, Javed

doi:10.1155/2018/3249720

Cited by 11 publications

(2 citation statements)

References 12 publications

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“…is the Atangana-Baleanu Caputo fractional derivative. The new iterative Laplace method (NILM), introduced in [36], is an improved version of the ADM method, which is used to solve nonlinear equations [37][38][39]. This does not need any calculation of Adomian polynomials in all its iterations.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

Alzahrani,

Abdoon,

Elbadri

et al. 2023

Symmetry

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This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines.

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Section: Introductionmentioning

confidence: 99%

A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

Alzahrani,

Abdoon,

Elbadri

et al. 2023

Symmetry

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show abstract

“…In the present work, coupled system of fractional-order differential equations will be solved using NIM. FDEs have been solved using NIM with the help of fractional derivative and integral operators [13,[15][16][17]. In this paper, we will find the solution of the Fractional Drinfeld-Sokolov-Wilson (FDSW) coupled system and fractional shallow water (FSW) coupled system.…”

Section: Introductionmentioning

confidence: 99%

New Iterative Method for Solving a Coupled System of Fractional‐Order Drinfeld–Sokolov–Wilson (FDSW) and Fractional Shallow Water (FSW) Equations

Ali

Yassen

Asiri

et al. 2022

Journal of Nanomaterials

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In this study, the new iterative method has been applied to a coupled system of fractional-order Drinfeld–Sokolov–Wilson (FDSW) and fractional shallow water (FSW) equations. The fractional-order derivatives are taken in the Caputo sense whose order is between 0 and 1. The suggested method is capable to handle the FDEs without any transformation and discretization. The obtained results have been compared with the exact solution and with the q-homotopy analysis transform method. The outcomes show the efficiency and effectiveness of NIM by comparing through tables and graphs.

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Explore dynamical soliton propagation to the fractional order nonlinear evolution equation in optical fiber systems

Zaman,

Arefin,

Akbar

et al. 2023

Opt Quant Electron

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New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma‐Tasso‐Olver Equations

Cited by 11 publications

References 12 publications

A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

New Iterative Method for Solving a Coupled System of Fractional‐Order Drinfeld–Sokolov–Wilson (FDSW) and Fractional Shallow Water (FSW) Equations

Explore dynamical soliton propagation to the fractional order nonlinear evolution equation in optical fiber systems

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