Approximate analytical solutions for a class of generalized perturbed KdV-burgers equation

Deng, Shaoqiang; Deng, Zihao

doi:10.2298/tsci2303881d

THERM SCI

2023

DOI: 10.2298/tsci2303881d

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Approximate analytical solutions for a class of generalized perturbed KdV-burgers equation

Shaoqiang Deng

Zihao Deng

Abstract: In this paper, we establish an efficient algorithm for solving a class of generalized perturbed KdV-Burgers equation with conformable time fractional derivative and He?s space fractal derivative. An illustrative example is presented.

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2024

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VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

GUAN,

GEPREEL,

2024

Fractals

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Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.

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VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

GUAN,

GEPREEL,

2024

Fractals

View full text Add to dashboard Cite

show abstract

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Approximate analytical solutions for a class of generalized perturbed KdV-burgers equation

Abstract: In this paper, we establish an efficient algorithm for solving a class of generalized perturbed KdV-Burgers equation with conformable time fractional derivative and He?s space fractal derivative. An illustrative example is presented.

Cited by 1 publication

References 38 publications

VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

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