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

Zhuo LiDepartment of Mechanical Engineering, School of Engineering, University of California, Merced, CA, USA

Lu LiuDepartment of Mechanical Engineering, School of Engineering, University of California, Merced, CA, USA;College of Information Science and Technology, Northeastern University, Shenyang, Liaoning Province, China

Sina DehghanDepartment of Mechanical Engineering, School of Engineering, University of California, Merced, CA, USA

YangQuan ChenDepartment of Mechanical Engineering, School of Engineering, University of California, Merced, CA, USA;Mechatronics, Embedded Systems and Automation Laboratory (MESA Lab), University of California, Merced, CA, USACorrespondence[email protected]

Dingyü XueCollege of Information Science and Technology, Northeastern University, Shenyang, Liaoning Province, China

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.

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