Modeling a Dynamic System Using Fractional Order Calculus

Fractional calculus is the integration and differentiation to an arbitrary or fractional order. The techniques of fractional calculus are not commonly taught in engineering curricula since physical laws are expressed in integer order notation. Dr. Richard Magin (2006) notes how engineers occasionally encounter dynamic systems in which the integer order methods do not properly model the physical characteristics and lead to numerous mathematical operations. In the following study, the application of fractional order calculus to approximate the angular position of the disk oscillating in a Newtonian fluid was experimentally validated. The proposed experimental study was conducted to model the nonlinear response of an oscillating system using fractional order calculus. The integer and fractional order mathematical models solved the differential equation of motion specific to the experiment. The experimental results were compared to the integer order and the fractional order analytical solutions. The fractional order mathematical model in this study approximated the nonlinear response of the designed system by using the Bagley and Torvik fractional derivative. The analytical results of the experiment indicate that either the integer or fractional order methods can be used to approximate the angular position of the disk oscillating in the homogeneous solution. The following research was in collaboration with Dr. Richard Mark French, Dr. Garcia Bravo, and Rajarshi Choudhuri, and the experimental design was derived from the previous experiments conducted in 2018.