Analytical solutions of some mathematical models involving beta fractional derivative

This thesis study consists of four chapters. In the first chapter, the concept of fractional derivative, its development, some special functions related to fractional derivative, various definitions of fractional derivative, and the studies in the literature regarding this derivative concept are mentioned. In the second part, the principle of homogeneous balance technique, which plays an important role in finding analytical solutions of some mathematical models containing Beta fractional derivatives, is clearly expressed, and the Modified Kudryashov method is discussed. The third part contains the original part of the thesis. The first of the four different beta fractional order equations is Chafee-Infante and the others are Geophysical KdV, shallow water wave, Gilson–Pickering equations. Here, the exact solutions of the equations were obtained using the Modified Kudryashov method, and three-dimensional graphs of the obtained solutions are included under each solution. In the fourth part, conclusions and recommendations are given.