Bright soliton solutions for time fractional Korteweg-de Vries equation

Özkan, Erdoğan Mehmet; Özkan, Ayten

doi:10.1063/5.0040280

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…Inc et al acquired new numerical solutions of fractional-time KdV equation by a technique of fictitious time integration and group preserving [45]. Authors in [46][47][48] used algebraic computational methods such as the modified extended tanh method, Sardar-subequation method, and He's semi-inverse variation method and the ansatz method to construct some soliton solutions of the nonlinear time-fractional KdV equation.…”

Section: Time-fractional Inhomogeneous Kdv Equationmentioning

confidence: 99%

Bivariate Chebyshev Polynomials to Solve Time‐Fractional Linear and Nonlinear KdV Equations

Zahrani

Matinfar

Eslami

2022

Journal of Mathematics

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This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. The fractional derivative operators are of the Caputo type. Two-variable second-kind Chebyshev wavelets (SKCWs) are constructed using one-variable ones; then, utilizing corresponding integral operational matrices leads to an approximate solution to the problem under study. Also, it is found that the perturbation term tends to zero even if a finite number of the basis functions is adopted. To exhibit the applicability and efficiency of the proposed scheme, two models of the KdV equations are given.

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Section: Time-fractional Inhomogeneous Kdv Equationmentioning

confidence: 99%

Bivariate Chebyshev Polynomials to Solve Time‐Fractional Linear and Nonlinear KdV Equations

Zahrani

Matinfar

Eslami

2022

Journal of Mathematics

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“…Time-Fractional Korteweg-de Vries (KdV) Equation has been applied with Riemann-Liouville fractional derivative in [53].…”

Section: Application Of Ammentioning

confidence: 99%

The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta-Derivative

Özkan

2021

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Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz method have been applied to find the soliton solutions for fractional Korteweg–de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by Atangana’s conformable derivative (beta-derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.

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Bright soliton solutions for time fractional Korteweg-de Vries equation

Cited by 2 publications

References 19 publications

Bivariate Chebyshev Polynomials to Solve Time‐Fractional Linear and Nonlinear KdV Equations

Bivariate Chebyshev Polynomials to Solve Time‐Fractional Linear and Nonlinear KdV Equations

The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta-Derivative

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