New hyperbolic structures for the conformable time-fractional variant bussinesq equations

Ali, Khalid K.; Nuruddeen, Rahmatullah Ibrahim; Raslan, K. R.

doi:10.1007/s11082-018-1330-6

Cited by 35 publications

(18 citation statements)

References 35 publications

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“…There are many papers that solve the nonlinear models, whether it is an analytical or numerical solution, but through our follow‐up, to this papers, we found that dealing with mathematical models in one dimension is easily either numerically or analytically, either when the model is in more than one dimension, we sometimes find it difficult to deal almost with it [1–13]. For this reason, most researchers began to deal with these models numerically.…”

Section: Introductionmentioning

confidence: 98%

On n‐dimensional quadratic B‐splines

Raslan

Ali

2020

Numerical Methods Partial

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In this paper, we present new constructions of the n‐dimensional quadratic B‐splines method. The quadratic B‐splines method format is displayed in a single, two, and three‐dimensional format. These constructions are of utmost importance in solving differential equations in their various dimensions, which have applications in many fields of science. Some numerical examples are also presented, through which we can show the accuracy of this construction by giving some comparisons of our results using this new construction and between the results in other works. Some figures also give in this paper for the solutions.

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Section: Introductionmentioning

confidence: 98%

On n‐dimensional quadratic B‐splines

Raslan

Ali

2020

Numerical Methods Partial

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“…In [7], conformable gradient vectors are defined, and a conformable sense Clairaut's theorem has also been proven. In [8][9][10][11][12][13][14], the researchers have worked on the linear ordinary and partial differential equations based on the conformable derivatives. Namely, two new results on homogeneous functions involving their conformable partial derivatives are introduced, specifically, homogeneity of the conformable partial derivatives of a homogeneous function and the conformable version of Euler's theorem.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

Bhanotar¹,

Kaabar

2021

International Journal of Differential Equations

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In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

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“…Korteweg-DeVries equation [14] can be a good example for dispersive waves. There are many equations developed for determining the wave behavior of a dynamical system [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For a small intersection of a spatiotemporal system the dynamics can be assumed as linear.…”

Section: Introductionmentioning

confidence: 99%

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

et al. 2021

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Rogue waves are very mysterious and extra ordinary waves. They appear suddenly even in a calm sea and are hard to be predicted. Although nonlinear Schrödinger equation (NLS) provides a perspective, it alone can neither detect rogue waves nor provide a complete solution to problems. Therefore, some approximations are still mandatory for both obtaining an exact solution and predicting rogue waves. Such as Kundu-Mukherjee-Naskar (KMN) model which allows obtaining lump-soliton solutions considered as rogue waves. In this study the functional variable method is utilized to obtain the analytical solutions of KMN model that corresponds to the propagation of soliton dynamics in optical fiber communication system.

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New hyperbolic structures for the conformable time-fractional variant bussinesq equations

Cited by 35 publications

References 35 publications

On n‐dimensional quadratic B‐splines

On n‐dimensional quadratic B‐splines

Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

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