Abstarct: In this thesis, fractional order sliding mode controllers baxsed on conformable derivative are designed. In addition, Lyapunov's direct method baxsed on conformable fractional order derivative is presented. One of the most advantages of conformable fractional order derivative is simple calculation due to similarity to integer one and having some of its properties which other definitions can not satisfied. With respected to the above benefits, application of conformable derivative in control design has proposed a new idea in control engineering. First, in order to investigate the stability of proposed controllers, Lyapunov's direct method baxsed on conformable derivative is presented. In the following, three typs of new fractional order sliding mode controllers baxsed on conformable derivatives are proposed. The designed controllers contain novel sliding surfaces as well as new switiching functions. They can improve the control performance such as increasing convergence speed, chattering reduction, decreasing control effort and simplifying calculation. Also, the simulation results confirm the effectiveness of the proposed controllers.