Yusuf Pandir

The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation

The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of .

The Extended Trial Equation Method for Some Time Fractional Differential Equations

Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractional equation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions.

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.

Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation

In this paper, we study the Kadomtsev–Petviashvili equation with generalized evolution and derive some new results using the approach called the trial equation method. The obtained results can be expressed by the soliton solutions, rational function solutions, elliptic function solutions and Jacobi elliptic function solutions. In the discussion, we give a new version of the trial equation method for nonlinear differential equations.

Modified Trial Equation Method to the Nonlinear Fractional Sharma-Tasso-Olever Equation

In this paper, we apply the modified trial equation method to fractional partial differential equations. The fractional partial differential equation can be converted into the nonlinear non-fractional ordinary differential equation by the fractional derivative and traveling wave transformation. So, we get some traveling wave solutions to the time-fractional Sharma-Tasso-Olever (STO) equation by the using of the complete discrimination system for polynomial method. The acquired results can be demoted by the soliton solutions, single-king solution, rational function solutions and periodic solutions. Index Terms—The modified trial equation method, fractional Sharma-Tasso-Olever equation, soliton solution, periodic solutions.

Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order

The main goal of the present research, the Modified Kudryashov Method has been used to obtain the exact solutions of Generalized Fisher Equation with fractional order. This approach has been newly submitted to the literature to obtain analytical solutions of nonlinear partial differential equations. In recent years, it has been aroused deep and comprehensive interest among scientists. This trend is largely because it is obtaining analytical solutions such as soliton solutions, hyperbolic function solutions and elliptic function solutions of fractional differential equations. When it comes to this study, we have applied Modified Kudryashov Method to obtain exact solution of Generalized Fisher Equation with fractional order in that it is hyperbolic Fibonacci function. The results obtained via this technique have been given for interpretation of the solutions which is modeling of equations.

New Exact Solutions of the Time-Fractional Nonlinear Dispersive KdV Equation

In this study, new version of the extended trial equation method is applied the nonlinear fractional partial differential equations. The fractional partial differential equations can be turned into the nonlinear non-fractional ordinary differential equations by the fractional derivative and traveling wave transformation. So, we find some traveling wave solutions to the time-fractional nonlinear dispersive KdV equation by the using of the complete discrimination system for polynomial method. As a result, these exact solutions to this nonlinear problem are constructed such as single king solution and hyperbolic function solutions.

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.

A multiple extended trial equation method for the fractional Sharma-Tasso-Olver equation

In this paper, a multiple extended trial equation method is proposed to seek exact solutions of nonlinear time-fractional equation. The validity and advantages of the proposed method are illustrated by its application to the Sharma-Tasso-Olver equation. As a result, various complexiton solutions consisting of hyperbolic functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution.