Computational Technique to Study Analytical Solutions to the Fractional Modified KDV-Zakharov-Kuznetsov Equation

Abdoon, Mohamed A.; Hasan, Faeza Lafta; Taha, Nidal E.

doi:10.1155/2022/2162356

Cited by 16 publications

(13 citation statements)

References 24 publications

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“…Engineers may be able to improve the performance of current systems and create more resilient designs that can manage nonlinear dynamics by utilizing the ABC-FD method. We suggested using this approach to tackle brand-new fractional problems [7,10,41] and contrasting numerical solutions with other approaches [6,19,[26][27][28].…”

Section: Discussionmentioning

confidence: 99%

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

Boulehmi

2024

Eur. J. Pure Appl. Math.

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This study aims to use a novel scheme for the Atangana-Baleanu Caputo fractional derivative (ABC-FD) to solve the fractional Bernoulli equation and the fractional R ̈ossler model. Furthermore, the suggested technique is compared to Runge-Kutta Fourth Order (RK4). The proposed method is efficacious and generates solutions that are indistinguishable from the approx-imate solutions generated by the RK4 method. Therefore, we can adapt the approach to various systems and develop results that are more accurate. On top of that, the new technique (ABC-FD) can identify chaotic situations. Consequently, this approach can be used to enhance the performance of other systems. In the future, this technique can be employed to determine the numerical solution for a multitude of models applicable in the fields of science and engineering.

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Section: Discussionmentioning

confidence: 99%

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

Boulehmi

2024

Eur. J. Pure Appl. Math.

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“…In many branches of engineering and the study of physics, see [1][2][3][4][5], fractional differential equations are commonplace. Many methods have been tried and tested in an effort to investigate and resolve fractional differential equations [6][7][8][9][10][11][12]. Together with advances in symbolic programming and new computing algorithms, the past few decades have seen the discovery of a plethora of novel methods for solving nonlinear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Solution of Generalized Caputo Fractional Initial Value Problems

et al. 2023

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In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented technique is considered to be an extension to the original Adams–Bashforth–Moulton approach. Numerical simulations and figures are presented and discussed, in order to show the efficiency of the proposed method. In the future, we anticipate that the provided generalized Caputo fractional derivative and the suggested method will be utilized to create and simulate a wide variety of generalized Caputo-type fractional models. We have included examples to demonstrate the accuracy of the present method.

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“…For this reason, the importance of the relevant model becomes high. Some studies on the equation are as follows: Exact solutions of time-fractional mKdV-ZK with undetermined coefficients method [16], Painleve analysis and wave profiles of model [17], obtaining soliton solution via modified extended mapping method [18], via ( ) ( ) tan 2 f x method [19], improved fractional sub-equation method [20], first integral method [21], functional variable method [22], investigation of the conservation laws on the model [23] and Lie symmetry analysis of the model [24] etc.…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Onder,

Secer,

Bayram

2023

Phys. Scr.

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In this paper, we explore analytical solutions for the (3+1)-dimensional time-fractional modified Korteweg–de Vries Zakharov-Kuznetsov equation, which incorporates a conformable derivative. Our interest in this model is driven by its significant role in simulating ion-acoustic waves in magnetized plasma. We adopt the unified Riccati equation expansion method and the new Kudrashov method to discover soliton solutions. Our approach uncovers various soliton types, such as kink, singular, periodic-singular, and bright solitons. We conduct a thorough analysis of how different parameters affect wave propagation, enhancing our study with descriptive figures and insightful observations. Furthermore, we delve into the modulation instability characteristic of this model. The influence of specific parameters, like wave number and the order of the conformable derivative, on wave dynamics is demonstrated through detailed visualizations. We also present 2D and 3D graphical representations of these solutions.

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Computational Technique to Study Analytical Solutions to the Fractional Modified KDV-Zakharov-Kuznetsov Equation

Cited by 16 publications

References 24 publications

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

A Numerical Solution of Generalized Caputo Fractional Initial Value Problems

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

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