The main goal of this thesis is to use Bernstein iterative method for solving a class of fractional differential equations. First, we try to study the existence and uniqueness of the solution to such problems. Then, in order to start the method, the main interval is divided into some subintervals. These subintervals help us to introduce the iterative steps in which the sequence of successive approximations is generated by approximating Bernstein polynomials. Some examples are included to show the efficiency and accuracy of this new technique.
