Non-commensurate fractional linear systems: New results

Optimal charging of fractional-order circuits with Cuckoo search

INTRODUCTION

Optimal charging of RC circuits is a well-studied problem in the integer-order domain due to its importance from economic and system temperature hazards perspectives. However, the fractional-order counterpart of this problem requires investigation.

OBJECTIVES

This study aims to find approximate solutions of the most energy-efficient input charging function in fractional-order RC circuits.

METHODS

This paper uses a meta-heuristic optimization technique called Cuckoo search optimizer to attain the maximum charging efficiency of three common fractional-order RC circuits. An analytical expression of the fractional capacitor voltage is suggested such that it satisfies the boundary conditions of the optimal charging problem. The problem is formulated as a fractional-order calculus of variations problem with compositional functional. The numerical solutions are obtained with the meta-heuristic optimization algorithm's help to avoid the complexities of the analytical approach.

RESULTS

he efficiency surfaces and input voltage charging curves are discussed for fractional-order in the range 0.5 < α ≤ 1 .

CONCLUSION

The optimized charging function can approximate the optimal charging curve using at most 4 terms. The charging time and the resistive parameters have the most dominant effect on charging efficiency at constant fractional-order α .

Fractional and fractal processes applied to cryptocurrencies price series

•

The dynamics of the cryptocurrencies is analyzed.

•

Several tools for investigating the dynamic behavior of the cryptocurrencies are adopted.

•

Characteristics of the cryptocurrencies price time series such as persistence, randomness, predictability and chaoticity are addressed.

•

With exception of for the Bitcoin, the other five cryptocurrencies analyzed are mean reverting.

Introduction

Cryptocurrencies have been attracting the attention from media, investors, regulators and academia during the last years. In spite of some scepticism in the financial area, cryptocurrencies are a relevant subject of academic research.

Objectives

In this paper, several tools are adopted as an instrument that can help market agents and investors to more clearly assess the cryptocurrencies price dynamics and, thus, guide investment decisions more assertively while mitigating risks.

Methods

We consider three methods, namely the Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) and Detrended Fluctuation Analysis, and three indices given by the Hurst and Lyapunov exponents or the Fractal Dimension. This information allows assessing the behaviour of the time series, such as their persistence, randomness, predictability and chaoticity.

Results

The results suggest that, except for the Bitcoin, the other cryptocurrencies exhibit the characteristic of mean reverting, showing a lower predictability when compared to the Bitcoin. The results for the Bitcoin also indicate a persistent behavior that is related to the long memory effect.

Conclusions

The ARFIMA reveals better predictive performance than the ARIMA for all cryptocurrencies. Indeed, the obtained residual values for the ARFIMA are smaller for the auto and partial auto correlations functions, as well as for confidence intervals.