Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods

This paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlin...

Full description

Saved in:
Bibliographic Details
Main Authors: Asad Freihat, Mohammed Alabedalhadi, Shrideh Al-Omari, Sharifah E. Alhazmi, Shaher Momani, Mohammed Al-Smadi
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Fractal and Fractional
Subjects:
Online Access:https://www.mdpi.com/2504-3110/9/3/152
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850205186846359552
author Asad Freihat
Mohammed Alabedalhadi
Shrideh Al-Omari
Sharifah E. Alhazmi
Shaher Momani
Mohammed Al-Smadi
author_facet Asad Freihat
Mohammed Alabedalhadi
Shrideh Al-Omari
Sharifah E. Alhazmi
Shaher Momani
Mohammed Al-Smadi
author_sort Asad Freihat
collection DOAJ
description This paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlinear ion acoustic waves and thus helping us to understand wave dynamics in plasmas. We introduce a new approach that relies on a new fractional expansion in the natural transform space and residual power series method to construct analytical solutions to the governing models. We investigate the theoretical analysis of the proposed method for these equations to expose this approach’s applicability, efficiency, and effectiveness in constructing analytical solutions to the governing equations. Moreover, we present a comparative discussion between the solutions derived during the work and those given in the literature to confirm that the proposed approach generates analytical solutions that rapidly converge to exact solutions, which proves the effectiveness of the proposed method.
format Article
id doaj-art-108e2a54a04343be84c0ee174cca6dcd
institution OA Journals
issn 2504-3110
language English
publishDate 2025-02-01
publisher MDPI AG
record_format Article
series Fractal and Fractional
spelling doaj-art-108e2a54a04343be84c0ee174cca6dcd2025-08-20T02:11:09ZengMDPI AGFractal and Fractional2504-31102025-02-019315210.3390/fractalfract9030152Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series MethodsAsad Freihat0Mohammed Alabedalhadi1Shrideh Al-Omari2Sharifah E. Alhazmi3Shaher Momani4Mohammed Al-Smadi5Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanDepartment of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanDepartment of Mathematics, College of Education for Girls at Al-Qunfudah, Umm Al-Qura University, Mecca 11942, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jordan, Amman 11942, JordanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanThis paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlinear ion acoustic waves and thus helping us to understand wave dynamics in plasmas. We introduce a new approach that relies on a new fractional expansion in the natural transform space and residual power series method to construct analytical solutions to the governing models. We investigate the theoretical analysis of the proposed method for these equations to expose this approach’s applicability, efficiency, and effectiveness in constructing analytical solutions to the governing equations. Moreover, we present a comparative discussion between the solutions derived during the work and those given in the literature to confirm that the proposed approach generates analytical solutions that rapidly converge to exact solutions, which proves the effectiveness of the proposed method.https://www.mdpi.com/2504-3110/9/3/152fractional modelplasma physicsKorteweg–deVries equationnatural transformresidual power series method
spellingShingle Asad Freihat
Mohammed Alabedalhadi
Shrideh Al-Omari
Sharifah E. Alhazmi
Shaher Momani
Mohammed Al-Smadi
Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
Fractal and Fractional
fractional model
plasma physics
Korteweg–deVries equation
natural transform
residual power series method
title Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
title_full Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
title_fullStr Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
title_full_unstemmed Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
title_short Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
title_sort certain analytic solutions for time fractional models arising in plasma physics via a new approach using the natural transform and the residual power series methods
topic fractional model
plasma physics
Korteweg–deVries equation
natural transform
residual power series method
url https://www.mdpi.com/2504-3110/9/3/152
work_keys_str_mv AT asadfreihat certainanalyticsolutionsfortimefractionalmodelsarisinginplasmaphysicsviaanewapproachusingthenaturaltransformandtheresidualpowerseriesmethods
AT mohammedalabedalhadi certainanalyticsolutionsfortimefractionalmodelsarisinginplasmaphysicsviaanewapproachusingthenaturaltransformandtheresidualpowerseriesmethods
AT shridehalomari certainanalyticsolutionsfortimefractionalmodelsarisinginplasmaphysicsviaanewapproachusingthenaturaltransformandtheresidualpowerseriesmethods
AT sharifahealhazmi certainanalyticsolutionsfortimefractionalmodelsarisinginplasmaphysicsviaanewapproachusingthenaturaltransformandtheresidualpowerseriesmethods
AT shahermomani certainanalyticsolutionsfortimefractionalmodelsarisinginplasmaphysicsviaanewapproachusingthenaturaltransformandtheresidualpowerseriesmethods
AT mohammedalsmadi certainanalyticsolutionsfortimefractionalmodelsarisinginplasmaphysicsviaanewapproachusingthenaturaltransformandtheresidualpowerseriesmethods