A behavioral analysis of KdVB equation under the law of Mittag–Leffler function

Goufo, Emile Franc Doungmo; Tenkam, H.M.; Khumalo, M.

doi:10.1016/j.chaos.2019.05.020

Cited by 17 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…under boundary conditions (2), using techniques adopted in the proof of Theorem 1, we also obtain criteria to ensure the SISP and SOSP for system (1). Under boundary control input (20), system (1) with boundary output (3) achieves the SISP if there are a constant K and a scalar 𝜆 1 > 0 satisfy the following conditions:…”

Section: Passivity-based Boundary Controlmentioning

confidence: 99%

“…Korteweg-de Vries-Burgers (KdVB) equations are the simplest third-order nonlinear partial differential equations (PDEs) with dispersion and dissipation. It covers models in the area of physics including solitons, shock propagation, dust-acoustic, and drift waves in plasma [1][2][3][4]. In recent decades, many significant works have been reported on stabilization of KdVB equations [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

Liang,

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

The passivity‐based boundary control is considered for stochastic Korteweg–de Vries–Burgers (SKdVB) equations. Both the stochastic input strictly passive (SISP) and stochastic output strictly passive (SOSP) are studied. By introducing Lyapunov functionals and Wirtinger's inequality, sufficient criteria are derived to establish SISP and SOSP for SKdVB equations with boundary disturbances. Moreover, when parameter uncertainties arise in SKdVB equations, the robust stochastic passivity is also investigated and sufficient criteria are presented to achieve the robust SISP and SOSP. Two numerical simulations are employed to show the effectiveness and advantages of our theoretical results.

show abstract

Section: Passivity-based Boundary Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

Liang,

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…It must be noted that the study of the model's existence, uniqueness, and stability analysis of model ( 1) has been previously studied. The reader can refer to references [30,31].…”

Section: Introductionmentioning

confidence: 99%

Analytical Approximate Solutions of Caputo Fractional KdV‐Burgers Equations Using Laplace Residual Power Series Technique

Burqan,

Khandaqji,

Al-Zhour

et al. 2024

Journal of Applied Mathematics

View full text Add to dashboard Cite

The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method.

show abstract

“…Abdo et al [24] and Kumar et al [25] have analysed three species of predatorprey models and the Fornberg-Whitham equation, respectively, by incorporating a fractional derivative with the ML type kernel. Combining the ABF derivative, the authors in [26] have explored the two-level perturbed Korteweg-de Vries Burgers equation.…”

Section: Introductionmentioning

confidence: 99%

Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel

Baishya

Veeresha

2021

Proc. R. Soc. A.

View full text Add to dashboard Cite

The Atangana–Baleanu derivative and the Laguerre polynomial are used in this analysis to define a new computational technique for solving fractional differential equations. To serve this purpose, we have derived the operational matrices of fractional integration and fractional integro-differentiation via Laguerre polynomials. Using the derived operational matrices and collocation points, we reduce the fractional differential equations to a system of linear or nonlinear algebraic equations. For the error of the operational matrix of the fractional integration, an error bound is derived. To illustrate the accuracy and the reliability of the projected algorithm, numerical simulation is presented, and the nature of attained results is captured in diverse order. Finally, the achieved consequences enlighten that the solutions obtained by the proposed scheme give better convergence to the actual solution than the results available in the literature.

show abstract

A behavioral analysis of KdVB equation under the law of Mittag–Leffler function

Cited by 17 publications

References 19 publications

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

Analytical Approximate Solutions of Caputo Fractional KdV‐Burgers Equations Using Laplace Residual Power Series Technique

Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel

Contact Info

Product

Resources

About