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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.

Partial differential equations are prevalently used as models to identify numerous physical occurrences and have a very crucial role in many sciences. Burgers equation, which is one type of partial differential equations, was first presented by Burgers in 1948 as a model for turbulent phenomena of viscous fluids [

The Cahn-Hilliard equation, which is one type of partial differential equations, was first introduced in 1958 as a model for process of phase seperation of a binary alloy under the critical temperature [

Korteweg-de Vries (KdV) equation, which is one type of partial differential equations, has been utilized to define a wide range of physical phenomena as a model for the evolution and interaction of nonlinear waves. It was derived as an evolution equation that conducting one-dimensional, small amplitude, long surface gravity waves propagating in a shallow channel of water [

The enquiry of exact solutions to nonlinear fractional differential equations has a very crucial role in several sciences such as physics, viscoelasticity, signal processing, probability and statistics, finance, optical fibers, mechanical engineering, hydrodynamics, chemistry, solid state physics, biology, system identification, fluid mechanics, electric control theory, thermodynamics, heat transfer, and fractional dynamics [

Our goal in this work is to introduce the exact solutions of time-fractional Burgers equation [

Recently, some authors have investigated Kudryashov method [

We consider the following nonlinear partial differential equation with fractional order for a function

The basic phases of the generalized Kudryashov method are explained as follows.

First of all, we must get the travelling wave solution of (

Suggest that the exact solutions of (

Under the terms of proposed method, we suppose that the solution of (

Replacing (

In this chapter, we search the exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV by using the generalized Kudryashov method.

We take the travelling wave solutions of (

The exact solutions of (

Consider

Consider

Consider

Consider

Consider

Consider

The exact solutions of (

We take the travelling wave solutions of (

The solutions given by (

We get the travelling wave solutions of (

The solutions given by (

We plot solution (

Graph of the solution (

Two-dimensional graph of the solution (

Graph of the solution (

Two-dimensional graph of the solution (

Graph of the solution (

Two-dimensional graph of the solution (

Graph of the solution (

Two dimensional graph of the solution (

Graph of the solution (

Two-dimensional graph of the solution (

Graph of the solution (

Two-dimensional graph of the solution (

Graph of the solution (

Two-dimensional graph of the solution (

Graph of the solution (

Two-dimensional graph of the solution (

The Kudryashov method provides us with the evidential manner to constitute solitary wave solutions for a large category of nonlinear partial differential equations. Previously, many authors have tackled Kudryashov method. But, in this paper, we construct generalized form of Kudryashov method. This type of method will be newly considered in the literature to generate exact solutions of nonlinear fractional differential equations.

According to this information, we can conclude that GKM has an important role to find analytical solutions of nonlinear fractional differential equations. Also, we emphasize that this method is substantially influential and reliable in terms of finding new hyperbolic function solutions. We think that this method can also be implemented in other nonlinear fractional differential equations.

The authors declare that there is no conflict of interests regarding the publication of this paper.