scholarly journals The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method

2021 ◽  
Vol 53 (9) ◽  
Author(s):  
Melike Kaplan ◽  
Arzu Akbulut
Keyword(s):  
Generalized Kudryashov Method ◽  
Kudryashov Method

scholarly journals New soliton solutions of the system of equations for the ion sound and Langmuir waves

2016 ◽  
Vol 7 (1) ◽  
pp. 42-49
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Sound Wave ◽  
High Frequency ◽  
Ponderomotive Force ◽  
Soliton Solutions ◽  
Langmuir Wave ◽  
Dark Soliton ◽  
System Of Equations ◽  
Langmuir Waves ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

scholarly journals Generalized Kudryashov Method for Time-Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Yusuf Pandir ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Third Order ◽  
Hilliard Equation ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Cahn Hilliard Equation

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

scholarly journals A short review on analytical methods for fractional equations with he’s fractional derivative

2017 ◽  
Vol 21 (4) ◽  
pp. 1567-1574 ◽  
Author(s):  
Yan Wang ◽  
Yu-Feng Zhang ◽  
Jian-Gen Liu ◽  
Muhammad Iqbal
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Methods ◽  
Function Method ◽  
Solution Process ◽  
Short Review ◽  
Fractional Equations ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Fractional Differential

He?s fractional derivative is adopted in this paper, and analytical methods for fractional differential equations are briefly reviewed, two modifications of the exp-function method (the generalized Kudryashov method and generalized expo-nential rational function method) are emphasized, and fractional Benjamin-Bo-na-Mahony equation with He?s fractional derivative is used as an example to elucidate the solution process.

scholarly journals The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 771
Author(s):  
Yusuf Gurefe
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger equations defined by Atangana's comformable derivative using the general Kudryashov method. Firstly, Atangana's comformable fractional derivative and its properties are included. Then, by introducing the generalized Kudryashov method, exact solutions of nonlinear fractional partial differential equations (FPDEs), which can be expressed with the comformable derivative of Atangana, are classified. Looking at the results obtained, it is understood that the generalized Kudryashov method can yield important results in obtaining the exact solutions of FPDEs containing beta-derivatives.

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