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Fractional-order model of a non-linear inductor

Lopes A. M., Tenreiro-Machado J. A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 1

61--67

This paper adopts a fractional calculus perspective to describe a non-linear electrical inductor. First, the electrical impedance spectroscopy technique is used for measuring the impedance of the device. Second, the experimental data is approximated by means of fractional-order models. The results demonstrate that the proposed approach represents the inductor using a limited number of parameters, while highlighting its most relevant characteristics.

Dynamics of Commodities Prices : Integer and Fractional Models

David S. A., Machado J. A. T., Trevisan L. R., Inácio Jr. C. M. C., Lopes A. M.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

389--408

This paper examines the time series of four important agricultural commodities, namely the soybean, corn, coffee and sugar prices. Time series can exhibit long-range dependence and persistence in their observation. The long memory feature of data is a documented fact and there has been an increasing interest in studying such concepts in the perspective of economics and finance. In this work, we start by analyzing the time series of the four commodities by means of the Fractional Fourier Transform (FrFT) to unveil time-frequency patterns in the data. In a second phase, we apply Auto Regressive Integrated Moving Average (ARIMA) and Auto Regressive Fractionally Integrated Moving Average (ARFIMA) models for obtaining the spot price composition and predict future price. The ARFIMA process is a known class of long memory model, representing a generalization of the ARIMA algorithm. We compare the performances of the ARIMA and the ARFIMA models and we show that the ARFIMA has a superior performance for future price forecasting.