Fractance analog realization using one order Newton method

Fractional calculus is a novel powerful tool for non-linear signal processing. This paper realizes the arbitrary order fractance of fractional calculus based on one order Newton process by solving the positive real root of the n-order equation as the approximation of the fractance. The condition under which the one order Newton process can be convergent is discussed. For semi-order fractance realization, the Steffensen method is used to accelerate its iteration process, which shows a good performance. We compare our method with others and present the analog passive realizations scheme of the arbitrary order fractance in the end.