Abstract
Abstract The discretization of fractional-order differential operators is the key to the digital realization of fractional-order controllers. This paper proposes an improved second-order fractional differential equation operation method based on power series expansion. The algorithm's operation speed and accuracy performance are analyzed. The research found that the algorithm proposed in this paper is suitable for the fractional operation of arbitrary signals, including discrete data sequences whose mathematical model is unknown and the solution of linear systems.
Highlights
We have focused on the mathematical theory of fractional calculus (FOC)
Liu Applied Mathematics and Nonlinear Sciences 2021(aop) 1–10 function, this paper proposes an improved method based on the power series expansion (PSE) and the Tustin transformation
Based on the above analysis, this paper proposes an improved FOC algorithm based on PSE and Tustin transform and applies it to the solution of linear fractional systems
Summary
We have focused on the mathematical theory of fractional calculus (FOC) It was not until the mid and late 20th century that FOC theory was introduced and applied in some fields such as electrochemistry, rheology, signal processing, and power transmission theory. Based on the Tustin transformation theory and the analysis of the characteristics of the discrete generating function formula used for fractional operators, and using the Maclaurin series expansion of the binomial power. Liu Applied Mathematics and Nonlinear Sciences 2021(aop) 1–10 function, this paper proposes an improved method based on the power series expansion (PSE) and the Tustin transformation. The algorithm proposed in this paper is suitable for the fractional operation of arbitrary signals, including discrete data sequences whose mathematical model is unknown and the solution of linear systems
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