Abstarct: At first we introduce the basic necessary concepts in chapter one of this thesis. next in chapter two we express the fractional differentiation and integration, also after the introduction of Riemann-Liouville and Gru ̈nwald-Letnikov fractional differentiation, we explain the properties and relations of this differentiations. On chapter three we say the structure of Homotopy Perturbation Method . then we investigate the convergence of this method by some theorems and demonstrate of applications of this method for solving the functional equations . on chapter four we introduce the some special forms of fractional differential equations and then solving them by Homotopy Perturbation Method.