In this paper, a new type of iterative learning control systems with fractional order known as iterative learning control with fractional order derivative and iterative learning control with fractional proportional–derivative for linearized systems of single-link robot arm is introduced. First order derivative of classic Arimoto is used for tracking error in updating law of derivative iterative learning control. Suggested method in this paper implement tracking error for updating control law of iterative learning of fractional order. For the first time, nonlinear robot system is linearized by input feedback linearization. Then, convergence analysis of iterative learning control law of type PD^alpha is studied.In the next step, we define a criteria for parameters optimization of proposed controller by using Biogeography-based optimization algorithm. Both updating law of fractional order iterative learning control (D^alpha-type ILC and PD^alpha-type ILC) is applied on linearized robot arm and performance of both controller for different value of alpha is presented. For improving the performance of closed loop system, coefficient of fractional order iterative learning control (proportional and derivative coefficients) is optimized by BBO algorithm. Proposed iterative learning control is compared with common type of system.