Mohamed Reda Ali Mohamed
Asst. Professor
Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity
fractal and fractional • 2023
Publication Information
Authors
Rashid Ali
*
, Ahmed S. Hendy
2
, Mohamed R. Ali
3,4
, Ahmed M. Hassan
5
, Fuad A. Awwad
6
and Emad A. A. Ismail
Keywords
Fractional Kudryashov–Sinelshchikov Equation; Nonlinear fractional partial differential
equations; Conformable fractional derivatives; Solitons; Variable transformation
Journal
fractal and fractional
Publisher
Not Available
Volume
Not Available
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
In this research work, we investigate the complex structure of soliton in the Fractional
Kudryashov–Sinelshchikov Equation (FKSE) using conformable fractional derivatives. Our study
involves the development of soliton solutions using the modified Extended Direct Algebraic Method
(mEDAM). This approach involves a key variable transformation, which successfully transforms the
model into a Nonlinear Ordinary Differential Equation (NODE). Following that, by using a series
form solution, the NODE is turned into a system of algebraic equations, allowing us to construct
soliton solutions methodically. The FKSE is the governing equation, allowing for heat transmission
and viscosity effects while capturing the behaviour of pressure waves in liquid–gas bubble mixtures.
The solutions we discover include generalised trigonometric, hyperbolic, and rational functions with
kinks, singular kinks, multi-kinks, lumps, shocks, and periodic waves. We depict two-dimensional,
three-dimensional, and contour graphs to aid comprehension. These newly created soliton solutions
have far-reaching ramifications not just in mathematical physics, but also in a wide range of subjects
such as optical fibre research, plasma physics, and a variety of applied sciences.
Kudryashov–Sinelshchikov Equation (FKSE) using conformable fractional derivatives. Our study
involves the development of soliton solutions using the modified Extended Direct Algebraic Method
(mEDAM). This approach involves a key variable transformation, which successfully transforms the
model into a Nonlinear Ordinary Differential Equation (NODE). Following that, by using a series
form solution, the NODE is turned into a system of algebraic equations, allowing us to construct
soliton solutions methodically. The FKSE is the governing equation, allowing for heat transmission
and viscosity effects while capturing the behaviour of pressure waves in liquid–gas bubble mixtures.
The solutions we discover include generalised trigonometric, hyperbolic, and rational functions with
kinks, singular kinks, multi-kinks, lumps, shocks, and periodic waves. We depict two-dimensional,
three-dimensional, and contour graphs to aid comprehension. These newly created soliton solutions
have far-reaching ramifications not just in mathematical physics, but also in a wide range of subjects
such as optical fibre research, plasma physics, and a variety of applied sciences.