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The cart-pendulum system is a typical benchmark problem for testing various control algorithms. Basically, it is a Single Input Multi Output (SIMO) system which has two output variables to be controlled (pendulum-angle and cart-position) using a single input (input voltage to power amplifier). This paper presents application of fractional calculus to the design of controllers for such a system. The controllers are tuned for the desired loop-shaping requirements by formulating constrained optimization problem so as to meet the required cart-position and inverted pendulum status. The performance of the tuned controllers is investigated.