Similarities in a fifth-order evolution equation with and with no singular kernel

Goufo, Emile Franc Doungmo; Kumar, Sunil; Mugisha, Stella

doi:10.1016/j.chaos.2019.109467

Cited by 165 publications

(44 citation statements)

References 21 publications

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“…Putting these values in Equations (10) and (37) yields a solitary wave solution for Equation (1) as:…”

Section: Setmentioning

confidence: 99%

“…Some of these methods are the exp-function method [1], the Darboux transformation [2], the Lie group analysis [3], the modified simple equation method [4], the homogeneous balance scheme [5], the sine-cosine method, and the tanh-coth method. Some new and effective attempts at determining solutions of partial differential equations can be found in [6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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New Solutions of Gardner's Equation Using Two Analytical Methods

Ghanbari

Băleanu

2019

Front. Phys.

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This article introduces and applies new methods to determine the exact solutions of partial differential equations that will increase our understanding of the capabilities of applied models in real-world problems. With these new solutions, we can achieve remarkable advances in science and technology. This is the basic idea in this article. To accurately describe this, some exact solutions to the Gardner's equation are obtained with the help of two new analytical methods including the generalized exponential rational function method and a Jacobi elliptical solution finder method. A set of new exact solutions containing four parameters is reported. The results obtained in this paper are new solutions to this equation that have not been introduced in previous literature. Another advantage of these methods is the determination of the varied solutions involving various classes of functions, such as exponential, trigonometric, and elliptic Jacobian. The three-dimensional diagrams of some of these solutions are plotted with specific values for their existing parameters. By examining these graphs, the behavior of the solution to this equation will be revealed. Mathematica software was used to perform the computations and simulations. The suggested techniques can be used in other real-world models in science and engineering.

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“…Putting these values in Equations (10) and (37) yields a solitary wave solution for Equation (1) as:…”

Section: Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Solutions of Gardner's Equation Using Two Analytical Methods

Ghanbari

Băleanu

2019

Front. Phys.

View full text Add to dashboard Cite

show abstract

“…It is well known that several physical phenomena are described by nonlinear differential equations (both ODEs and PDEs). Therefore, the study of the many analytical and numerical methods used for solving the nonlinear differential equations is a very important topic for the analysis of engineering practical problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel

Afshari

Băleanu

2020

Adv Differ Equ

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“…For example, the Adomian decomposition method (Cheniguel, 2013), the optimal asymptotic homotopy method (Ullah et al, 2015), the Laplace Transform method (Oke, 2017), the high-order stereomodelling method (Tong, Yang, Hua, & Wang, 2013), the Variational Iteration Method (Biazar & Ghazvini, 2008), the new implicit second-order alternating direction method (Qin, 2009), the difference potential method (Britt, Tsynkov & Turkel, 2018), the fixed point iteration method, the Newton method (Shevchenko, 2008) and the local fractional variational iteration method (Jassim, 2015). In addition, there are many methods that provide an approximate solution for different types of differential equations (El-Ajou, Oqielat, Al-Zhour, Ghanbari, Kumar, & Kumar, 2020;Goufo, Kumar & Mugisha, 2020;Jleli, Kumar, Kumar & Samet, in press;Kumar, Kumar, Abbas, Al Qurashi & Baleanu, 2020;Kumar, Kumar, Momani, Aldhaifallah, & Nisar, 2019;Kumar, Nisar, Kumar, Cattani & Samet, in press).…”

Section: Introductionmentioning

confidence: 99%

Analytic and numerical solutions for linear and nonlinear multidimensional wave equations

Adwan

AL-Jawary

Tibaut

et al. 2020

Arab Journal of Basic and Applied Sciences

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We develop three reliable iterative methods for solving the nonlinear 1D, 2D and 3D second-order wave equation and compare the results with a discretization-based solver. The iterative Tamimi-Ansari method (TAM), Daftardar-Jafari method (DJM) and the Banach contraction method (BCM) are used to obtain the exact solution for linear equations. For nonlinear equations and practical problems, however, one obtains the approximate solutions that converge to the exact solution, if one exists. The convergence analysis of the three methods is shown using the fixed-point theorem. The methods prove to be quite efficient and well suited to solve this kind of problems. We present several examples that demonstrate the accuracy and efficiency of the methods. We also compare the methods with a method based on discretization (Boundary Domain Integral Method (BDIM)). The BDIM uses a standard domain grid and discretizes the integral form of the governing equations. The iterative methods were developed with MathematicaV R 10, while BDIM is a proprietary development. ARTICLE HISTORY

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Similarities in a fifth-order evolution equation with and with no singular kernel

Cited by 165 publications

References 21 publications

New Solutions of Gardner's Equation Using Two Analytical Methods

New Solutions of Gardner's Equation Using Two Analytical Methods

Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel

Analytic and numerical solutions for linear and nonlinear multidimensional wave equations

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