Abstract
The definitions and properties of widely used fractional-order derivatives are summarized in this paper. The characteristic polynomials of the fractional-order systems are pseudo-polynomials whose powers of the complex variable are non-integers. This kind of systems can be approximated by high-order integer-order systems, and can be analyzed and designed by the sophisticated integer-order systems methodology. A new closed-form algorithm for fractional-order linear differential equations is proposed based on the definitions of fractional-order derivatives, and the effectiveness of the algorithm is illustrated through examples.
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Translated from Journal of Northeastern University (Natural Science), 2007, 28(1): 10–13 [译自: 东北大学学报(自然科学版)]
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Zhao, C., Xue, D. Closed-form solutions to fractional-order linear differential equations. Front. Electr. Electron. Eng. Ch 3, 214–217 (2008). https://doi.org/10.1007/s11460-008-0025-3
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DOI: https://doi.org/10.1007/s11460-008-0025-3