Traveling wave solutions of conformable time-fractional Zakharov–Kuznetsov and Zoomeron equations

Odabaşı, Meryem

doi:10.1016/j.cjph.2019.11.003

Cited by 34 publications

(14 citation statements)

References 27 publications

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“…Also Liu proposed complete discrimination system (CDS) to find exact solutions of PDEs, see [17][18][19]. The method is studied by some authors [20][21][22][23] to investigate analytical solutions of integer and non-integer order partial differential equations.…”

Section: Conformable Fractional Derivative and Trial Solution Algorithmmentioning

confidence: 99%

Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

Odabaşı

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, exact analytical solutions of the biological population model, the EW and the modified EW equations with a conformable derivative operator have been examined by means of the trial solution algorithm and the complete discrimination system. Dark, bright and singular traveling wave solutions of the equations have been obtained by algorithm. Also, revealed singular periodic solutions have been listed. All solutions were verified by substituting them into their corresponding equation via Mathematica package program.

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Section: Conformable Fractional Derivative and Trial Solution Algorithmmentioning

confidence: 99%

Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

Odabaşı

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Recently, based on the approach proposed by Ma and Fuchssteiner [17], Cheng-Shi Liu [13]- [15] introduced the trial solution method that reduces the undertaking equation to solvable differential equations for solving nonlinear differential equations. Some authors [6], [19][20][21][22][23] applied this efficient procedure to some nonlinear evolution equations. In this study, among the methods used for nonlinear partial differential equations, the trial solution procedure is considered.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Exact Solutions of some Nonlinear Evolution Equations via an Analytical Approach

Odabaşı

2021

Mathematical Sciences and Applications E-Notes

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This study investigates exact analytical solutions of some nonlinear partial differential equations arising in mathematical physics. To this reason, the Kudryashov-Sinelshchikov equation, the ZK-BBM equation and the Gardner equation have been considered. With the implementation of the trial solution algorithm, solitary wave, bright, dark and periodic exact traveling wave solutions of the considered equations have been attained. The solutions have been checked and graphs have been given via package programs to see the behavior of the waves.

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“…Numerous methods have been applied to obtain different solutions of fractional partial differential equations. Some of them are; the functional variable method [7], the extended tanh function method [8], the first integral method [9], the extended direct algebraic method [10], the modified simple equation method [11], the modified trial equation method [12], the ( ′ / ) -expansion method [13], the extended trial equation method [14], the kudryashov method [15] and so on [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

On the Physical Behaviours of the Conformable Fractional Modified Camassa– Holm Equation Using Two Efficient Methods

Elma

Mısırlı

2021

ijmph

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In recent years, many authors have researched about fractional partial differential equations. Physical phenomena, which arise in engineering and applied science, can be defined more accurately by using FPDEs. Thus, obtaining exact solutions of the FPDEs equations have become more important to understand physical problems. In this article, we have reached the new traveling wave solutions of the conformable fractional modified Camassa -Holm equation via two efficient methods such as first integral method and the functional variable method. The wave transformation and conformable fractional derivative have been used to convert FPDE to the ordinary differential equation. The Camassa -Holm equation is physical model of shallow water waves with non-hydrostatic pressure. Thanks to these powerful methods, some comparisons, such as type of solutions and physical behaviours, have been made. Additionally, mathematica program have been used with the aim of checking of solutions. Investigating results of the fractional differential equations can help understanding complex phenomena in applied mathematics and physics.

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Traveling wave solutions of conformable time-fractional Zakharov–Kuznetsov and Zoomeron equations

Cited by 34 publications

References 27 publications

Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

Investigation of Exact Solutions of some Nonlinear Evolution Equations via an Analytical Approach

On the Physical Behaviours of the Conformable Fractional Modified Camassa– Holm Equation Using Two Efficient Methods

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