Hyperbolic trigonometric travelling wave solution for non-integer balancing term of partial differential equations

In this study, we aim to reach the analytical solution without using a new transformation to make the balancing term integer for both partial differential equations and fractional partial differential equations without the term integer. For this, cubic nonlinear Klein Gordon equation for a partial differential equation, time-fractional Eckhaus equation in fractional partial differential equation is taken into consideration. This presented method is new and is discussed for the first time in this study. This study consists of the following sections. The thesis consists of six chapters. In the first chapter, the history of nonlinear partial differential equations is given. In the second chapter, the basic definitions required for the thesis study are given. In the third chapter, using (1 / Gꞌ) - Expansion Method, this method can be applied for non-integer balancing terms of partial differential equations. In the fourth chapter, the exact solutions of the Eckhaus and cubic nonlinear Klein Gordon equation, and obtained new types of complex hyperbolic trigonometric travelling wave solution for the Eckhaus and cubic nonlinear Klein Gordon equation. In the fifth section, the findings obtained as a result of the studies are given. In the sixth chapter, a concluding discussion regarding the thesis is given. Keywords: Partial differential equation, hyperbolic trigonometric travelling wave solutions; non-integer balancing term.