Fractional Solution Of The Catenary Curve

The catenary curve has been used in a vast number of practical applications, and several mathematical models have been studied to approximate its behavior. This work, motivated by the success of fractional calculus, proposes a fractional model for the catenary curve, using the Caputo-Fabrizio (CF) definition. It was analyzed how the fractional derivative order and the fractional initial condition directly affect the hanging cable shape. It was noticed that the proposed model provides the possibility of describing new scenarios and revealing new information about the system. Therefore, this work gives rise to a new family of curves that can be used in any practical problem involving catenaries, varying at most two parameters.