A Novel Fractional Order Differentiator

The aim of this study is to analyze and design a novel fractional order differentiator which is robust against noise, this method allows to estimate the Caputo fractional order derivative of an unknown bounded noisy signal, also the original signal is estimated. In this sense, our proposal can reduce the effect of noise in the estimation of the original signal as well as in its fractional order derivative. The construction of this differentiator is based on a simple proportional-fractional order integral algorithm. Numerical simulations are performed considering the presence and absence of noise, showing the effectiveness, accuracy and robustness of our fractional order differentiator.