Novel exact solutions of the fractional Bogoyavlensky–Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative

Khater, Mostafa M. A.; Ghanbari, Behzad; Nisar, Kottakkaran Sooppy; Kumar, Devendra

doi:10.1016/j.aej.2020.03.032

Cited by 66 publications

(20 citation statements)

References 47 publications

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“…Due to its wide scope and diverse applications in different disciplines, the importance of exact (analytical) and numerical solutions of fractional differential equations has increased. Many methods such as the direct algebraic method (Rezazadeh et al 2017), the sinh-Gordon function method , the decomposition method (Ray 2006), the discrete homotopy perturbation method (Özpınar 2020), the finite forward difference method (Yokuş 2020), the modified homotopy analysis transform method (Morales-Delgado et al 2018), the ( + 1/ ′ )expansion method , the subequation method (Tasbozan et al 2019, the ( ′ / ) method (Durur 2020, Shang andZheng 2013), fractional sub-equation method (Yaşar and Yıldırım 2018), (1/G′)-expansion method (Durur ve Yokuş 2019, Durur ve Yokuş 2020, the generalization exponential rational method (Khater et al 2020), the modified auxiliary equation method (Alderremy et al 2019) etc. to be used to reach solutions have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Constructions Of Traveling Wave Solutions Of The Fractional Nonlinear Model Of The Low-Pass Electrical Transmission Lines

Yaşar¹

2021

Afyon Kocatepe University Journal of Sciences and Engineering

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In this article, the structure of the improved ( /2)-expansion method and the simplest equation method are applied. The fractional nonlinear model of the low-pass electrical transmission lines via Atangana-Baleanu derivative operator is taken into consideration and exact solutions have been constructed of this equation using proposed methods. This article explores the applicability and effectiveness of these methods on fractional nonlinear evolution equations.

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Section: Introductionmentioning

confidence: 99%

Constructions Of Traveling Wave Solutions Of The Fractional Nonlinear Model Of The Low-Pass Electrical Transmission Lines

Yaşar¹

2021

Afyon Kocatepe University Journal of Sciences and Engineering

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“…This plasma comprises of nonthermal ions and negatively charged mobile dust crystals, and q-distributed temperature electrons of distinct nonextensivity power [5]. The ZK equation's mathematical formula found by the well-known reductive disruption process [6] is given by Solving this kind of models has attracted many researchers in various areas, chemical physics [7], geochemistry [8], plasma physics [8], fluid mechanics [9], optical fiber [10], solid-state physics [11], and so on [12][13][14][15]. Consequently, constructing the exact solutions of these mathematical models is an indispensable tool for detecting novel properties of them that can be used in their various applications.…”

Section: Introductionmentioning

confidence: 99%

On the Analytical and Numerical Solutions in the Quantum Magnetoplasmas: The Atangana Conformable Derivative (1+3)-ZK Equation with Power-Law Nonlinearity

Khater

Chu

Attia

et al. 2020

Advances in Mathematical Physics

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In this research paper, our work is connected with one of the most popular models in quantum magnetoplasma applications. The computational wave and numerical solutions of the Atangana conformable derivative (1+3)-Zakharov-Kuznetsov (ZK) equation with power-law nonlinearity are investigated via the modified Khater method and septic-B-spline scheme. This model is formulated and derived by employing the well-known reductive perturbation method. Applying the modified Khater (mK) method, septic B-spline scheme to the (1+3)-ZK equation with power-law nonlinearity after harnessing suitable wave transformation gives plentiful unprecedented ion-solitary wave solutions. Stability property is checked for our results to show their applicability for applying in the model’s applications. The result solutions are constructed along with their 2D, 3D, and contour graphical configurations for clarity and exactitude.

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“…Equation ( 1) is also called the combined KdV-mKdV equation. In recent years, partial differential equations have become one of the most widely used fields of mathematics in various branches of science and engineering [5][6][7][8][9][10][11][12]. In this paper, the Gardner equation is examined by using the improved tan(Θ(ϑ))-expansion method and the wave ansatz method.…”

Section: Introductionmentioning

confidence: 99%

Exact Traveling Wave Solutions of the Gardner Equation by the Improved tanΘϑ-Expansion Method and the Wave Ansatz Method

Günerhan

2020

Mathematical Problems in Engineering

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Nonlinear partial differential equations (NLPDEs) are an inevitable mathematical tool to explore a large variety of engineering and physical phenomena. Due to this importance, many mathematical approaches have been established to seek their traveling wave solutions. In this study, the researchers examine the Gardner equation via two well-known analytical approaches, namely, the improved tanΘϑ-expansion method and the wave ansatz method. We derive the exact bright, dark, singular, and W-shaped soliton solutions of the Gardner equation. One can see that the methods are relatively easy and efficient to use. To better understand the characteristics of the theoretical results, several numerical simulations are carried out.

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Novel exact solutions of the fractional Bogoyavlensky–Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative

Cited by 66 publications

References 47 publications

Constructions Of Traveling Wave Solutions Of The Fractional Nonlinear Model Of The Low-Pass Electrical Transmission Lines

Constructions Of Traveling Wave Solutions Of The Fractional Nonlinear Model Of The Low-Pass Electrical Transmission Lines

On the Analytical and Numerical Solutions in the Quantum Magnetoplasmas: The Atangana Conformable Derivative (1+3)-ZK Equation with Power-Law Nonlinearity

Exact Traveling Wave Solutions of the Gardner Equation by the Improved tanΘϑ-Expansion Method and the Wave Ansatz Method

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