Seyma Tuluce Demiray

Generalized Kudryashov Method for Time-Fractional Differential Equations

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.

Exact solutions of nonlinear Schrodinger’s equation with dual power-law nonlinearity by extended trial equation method

In this paper, we acquire the soliton solutions of the nonlinear Schrodinger’s equation with dual power-law nonlinearity. Primarily, we use the extended trial equation method to find exact solutions of this equation. Then, we attain some exact solutions including soliton solutions, rational and elliptic function solutions of this equation using the extended trial equation method.

Some exact solutions of generalized Zakharov system

In this paper, we seek exact solutions of generalized Zakharov system. We use extended trial equation method to obtain exact solutions of this system. Consequently, we obtain some exact solutions including soliton solutions, rational, Jacobi elliptic and hyperbolic function solutions of this system by using extended trial equation method.

Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations

We make use of the so-called Sumudu transform method (STM), a type of ordinary differential equations with both integer and noninteger order derivative. Firstly, we give the properties of STM, and then we directly apply it to fractional type ordinary differential equations, both homogeneous and inhomogeneous ones. We obtain exact solutions of fractional type ordinary differential equations, both homogeneous and inhomogeneous, by using STM. We present some numerical simulations of the obtained solutions and exhibit two-dimensional graphics by means of Mathematica tools. The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions.

New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation

In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods.

New soliton solutions for Sasa–Satsuma equation

In this work, we survey exact solutions of Sasa–Satsuma equation (SSE). We utilize extended trial equation method (ETEM) and generalized Kudryashov method to acquire exact solutions of SSE. First of all, we gain some exact solutions such as soliton solutions, rational, Jacobi elliptic, and hyperbolic function solutions of SSE by means of ETEM. Furthermore, we procure dark soliton solution of this equation by the help of generalized Kudryashov method. Lastly, for certain parameter values, we draw two- and three-dimensional graphics of imaginary and real values of some exact solutions that we achieved using these methods.

The Investigation of Exact Solutions of Nonlinear Time-Fractional Klein-Gordon Equation by Using Generalized Kudryashov Method

In this study, we consider exact solutions of nonlinear time-fractional Klein-Gordon equation by using generalized Kudryashov method (GKM). The nonlinear time-fractional Klein-Gordon equation can be converted into nonlinear ordinary differantial equation by transformation. Consequently, GKM has been implemented to find exact solutions of nonlinear time-fractional Klein-Gordon equation and we obtain some new solutions such as soliton solutions and hyperbolic function solutions. Moreover, we point out that this method is a generalized form of classical Kudryashov Method.

The analysis of the exact solutions of the space fractional coupled KD equations

In this study, we seek exact solutions of the space fractional coupled Konopelchenko-Dubrovsky (KD) equations by using generalized Kudryashov method. The space fractional coupled KD equations can be converted into nonlinear ordinary differantial equation by transformation. Consequently,generalized Kudryashov method has been used to obtain exact solutions of the space fractional coupled KD equations. From hence, we find some new hyperbolic function solutions. Also, we emphasize that this method is a generalized form of classical Kudryashov Method.

Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus

The aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended equation was presented in detail. The uniqueness of the special solution was also investigated. A resume of the method for solving this equation was provided. The algorithm was used to derive the unique special solution for given initial conditions.

Soliton solutions of some nonlinear evolution problems by GKM

In this paper, we establish exact solutions of coupled Higgs equation and Nizhnik-Novikov-Veselov (NNV) system. We apply generalized Kudryashov method (GKM) to seek exact solutions of coupled Higgs equation and NNV system. We find dark soliton solutions of coupled Higgs equation and NNV system via GKM. Then, for proper parameters, we plot 2D and 3D surfaces of some dark soliton solutions that we obtained by using this method. Numerical results together with the graphical demonstrations clearly present the reliability of this method. Also, the proposed method is consonant with the physical structure of such equations.