Chaotic Analysis and Wave Photon Dynamics of Fractional Whitham–Broer–Kaup Model with <i>β</i> Derivative

Chaotic Analysis and Wave Photon Dynamics of Fractional Whitham–Broer–Kaup Model with <i>β</i> Derivative

This study uses a conformable derivative of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> to investigate a fractional Whitham–Broer–...

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Bibliographic Details
Main Authors:	Muhammad Idrees Afridi, Theodoros E. Karakasidis, Abdullah Alhushaybari
Format:	Article
Language:	English
Published:	MDPI AG 2025-04-01
Series:	Fractal and Fractional
Subjects:	fractional Whitham–Broer–Kaup model <i>β</i>-conformable derivative enhanced modified Sardar sub-equation approach wave dynamics of photons perturbed phase portraits non-perturbed phase portraits
Online Access:	https://www.mdpi.com/2504-3110/9/5/287
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Summary:	This study uses a conformable derivative of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> to investigate a fractional Whitham–Broer–Kaup (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FWBK</mi></semantics></math></inline-formula>) model. This model has significant uses in several scientific domains, such as plasma physics and nonlinear optics. The enhanced modified Sardar sub-equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">EMSSE</mi></semantics></math></inline-formula> approach is applied to achieve precise analytical solutions, demonstrating its effectiveness in resolving complex wave photons. Bright, solitary, trigonometric, dark, and plane waves are among the various wave dynamics that may be effectively and precisely determined using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FWBK</mi></semantics></math></inline-formula> model. Furthermore, the study explores the chaotic behaviour of both perturbed and unperturbed systems, revealing illumination on their dynamic characteristics. By demonstrating its validity in examining wave propagation in nonlinear fractional systems, the effectiveness and reliability of the suggested method in fractional modelling are confirmed through thorough investigation.
ISSN:	2504-3110