Numerical solutions of fractional partial differential equations with homotopy analysis method

This thesis consists of 7 parts. In the first part, the history of the homotopy analysis method and the related literature is reviewed. In the second part involves the basic definitions, theorems and preliminary information are used in this study. In the third chapter, information about homotopy analysis method and its development is analysed. In the fourth part, the numerical solutions of the nonlinear Burgers equation containing the fractional derivative in terms of Caputo have been obtained by using the homotopy analysis method and the charts and the graphs of this problem have been shown. In the fifth one, the numerical solutions of the nonlinear Advection equation containing the fractional derivative in terms of Caputo have been obtained by using homotopy analysis method and the chart and the graphs of this problem were given. In the sixth part, numerical solutions of linear and nonlinear Klein-Gordon equations containing fractional order from Caputo have been obtained by using homotopy analysis method. The charts and graphs of these problems were also demonstrated. The last part of this study consists of the conclusion and discussion of the thesis.