A Modified Fractional Calculus Approach to Model Hysteresis

This paper describes the development of a fractional calculus approach to model the hysteretic behavior shown by the variation in electrical resistances with strain in conductive polymers. Experiments have been carried out on a conductive polymer nanocomposite sample to study its resistance-strain variation under strain varying with time in a triangular manner. A combined fractional derivative and integer order integral model and a fractional integral model (with two submodels) have been developed to simulate this behavior. The efficiency of these models has been discussed by comparing the results, obtained using these models, with the experimental data. It has been shown that by using only a few parameters, the hysteretic behavior of such materials can be modeled using the fractional calculus with some modifications.