Solution of the nonlineer fractional order derivative partial differential equations with homotopy analysis method

The first chapter of this thesis consisting of four chapters is designed as introductory and a literature summary is presented.In the second chapter, after presenting some special functions, Grünwald-Letnikov, Riemann-Liouville and Caputo approximations which are used in the calculations of fractional order derivative and integral are given.In the third chapter, general concepts are given about Homotopy Analysis method and then Homotopy Analysis solutions of one-dimensional and two-dimensional heat transfer problem as an example of its application to partial differential equations.In the fourth chapter which is the main body of the thesis, Homotopy Analysis method is applied to fractional order one-dimensional heat transfer, two-dimensional heat transfer, Sharmo-Tasso-Olver and coupled Modified Korteweg de Vries (mKdV) equations given with initial conditions, and after determining the convergence range of each problem?s series solution, their numerical solutions are obtained.