Abstarct: Many of around phenomenon in the world are nonlinear and we can describe them by nonlinear equations. with the help of advanced computers; solving the linear problems is easy but in generally, it will be difficult to find the exact solution of nonlinear problems. In this thesis, our goal is to fined exact solution of nonlinear fractional differential equations by using of Kudryashov method. For this goal, we first introduce fractional caculus functions and express some of their properties; then we introduce the concept of derivative and integral with noninteger order and their relations and properties. Also we explain the classical Kudryashov method for equations. Finally we solve some type of nonlinear fractional differential equations by using of the generalized and modified Kudryashov method.