Fractional dynamics study: analytical solutions of modified Kordeweg-de Vries equation and coupled Burger’s equations using Aboodh transform

The study examines the using of Aboodh residual power series method and the Aboodh transform iteration method (ATIM) to analyze modified Korteweg-de Vries equation (mKdV) beside coupled Burger’s equations in the framework of the Caputo operator. These sets of equations represent the non-linear wave...

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Bibliographic Details
Published in:Scientific reports 2024-06, Vol.14 (1), p.12751-12751, Article 12751
Main Authors: Iqbal, Naveed, Hussain, Shah, Hamza, Amjad E., Abdullah, Ali, Mohammed, Wael W., Yar, Mohammad
Format: Article
Language:English
Subjects:
639/705/1041
639/705/1042
Aboodh residual power series method
Aboodh transform iteration method
Algorithms
Biology
Caputo operator
Coupled Burger’s equations
Engineering
Expansion
Fluid mechanics
Humanities and Social Sciences
Materials science
Mathematics
Methods
Modified Kordeweg-de Vries equation (mKdV)
multidisciplinary
Partial differential equations
Physics
Power
Science
Science (multidisciplinary)
Titanium alloys
Wave analysis
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Summary:The study examines the using of Aboodh residual power series method and the Aboodh transform iteration method (ATIM) to analyze modified Korteweg-de Vries equation (mKdV) beside coupled Burger’s equations in the framework of the Caputo operator. These sets of equations represent the non-linear wave description for various physical systems. Through APM and ATIM, the solution for the coupled Burger’s equations and the mKdV equation get accurate dynamics information that will reveal the nature of their interactions. Using mathematically proven techniques and computational simulations, the developed methods’ efficiency and reliability are illustrated in the complex behaviors of these nonlinear wave equations, so that we can gain deeper insights into their complex dynamics. The research is aimed at an increase of the knowledge about the fractional calculus utilization for nonlinear wave motion and it also provides analytical tools for an analysis of wave acting in different scientific and engineering areas.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-024-61972-w