The solution methods of linear and nonlinear fractional differential equations

This study consist of the five chapters. In Section 1, it has been given informations on the solution techniques and one the historical structures of differential equations with fractional order was given and some information on the solution techniques were also presented. In Section 2, some fundamental definitions and theorems which are necessary in this study was introduced. In Section 3, the general structures of Generalized Kudryashov Method (GKM), Sumudu Transform Method (STM), Variational Iteration Method (VIM) and Homotopi Decomposition Method, were given. In Section 4, Firstly GKM was used to obtain analytical solutions of nonlinear time-fractional Klein-Gordon equation, time-fractional KdV and mKdV equations, time-fractional second-order Burgers equation, time-fractional Cahn-Hilliard equation and time-fractional generalized third-order KdV equation. Secondly, STM was utilized to find analytical solutions of homogeneous and non-homogeneous fractional ordinary differential equations. Thirdly, VIM was handled to reach approximate solutions of homogeneous and non-homogeneous fractional ordinary differential equations. Finally, Homotopi Decomposition Method (HDM) was tackled to gain approximate solutions of fractional Kadomtsev-Petviashvili equation. Two and three dimensional graphics of analytical and approximate solutions that we obtained by the help of these methods were plotted by means of Mathematica programme. In chapter five, it has been given a conclusion about techniques used by taking into consideration analytical and approximate solutions obtained in this study.