Efficient and careful adjustment of dynamical properties of a system can be obtained by Fractional PI ^λ D ^μ Controller because there are five parameters compared with integer order PID controllers. Literature survey reveals that some attempts were mostly made to control the stable plants like speed control of DC Motors and pH neutralization chemical processes using these controllers. A typical cart-inverted pendulum control system on the other hand is unstable, non-minimum phase and highly non-linear with one input voltage of a DC Motor which can change the position of the cart and the angle of the inverted pendulum arm which makes the analysis of this system more efficacious to understand the different aspects and strategies of the control engineering. Based on the mathematical representation of the plant, a fractional order PI ^λ D ^μ controller is designed and verified in MATLAB to stabilize the unstable pendulum at its upright equilibrium point and to compare the performance of these fractional order PI ^λ D ^μ controllers over conventional integer order classical PID controller which confirms the effectiveness of the approach.