A review and evaluation of numerical tools for fractional calculus and fractional order control

TL;DR

This paper surveys and evaluates various numerical tools for fractional calculus and fractional order control, providing a comprehensive comparison to assist researchers in selecting appropriate methods.

Contribution

It compiles and assesses existing numerical tools for fractional calculus, offering a comparative analysis of their accuracy and performance for diverse applications.

Findings

Provides a dashboard view of available tools

Evaluates accuracy and performance of tools

Offers guidance for tool selection

Abstract

In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.