| [1] |
Torvik P J, Bagley R L. On the appearance of the fractional derivative in the behavior of real materials[J]. Journal of Applied Mechanics, 1984, 51(2): 294-298.
|
| [2] |
Caputo M. Distributed order differential equations modeling dielectric induction and diffusion[J]. Fractional Calculus and Applied Analysis, 2001, 4(4): 421-442.
|
| [3] |
Bisquert J, Compte A. Theory of the electrochemical impedance of anomalous diffusion[J]. Journal of Electroanalytical Chemistry, 2001, 499(1): 112-120.
|
| [4] |
赵元英, 袁晓, 滕旭东, 等. 常用周期信号的分数微分运算[J]. 四川大学学报: 工程科学版, 2004, 36(2): 94-97. Zhao Y Y, Yuan X, Teng X D, et al. Fractional order differentiation of periodical signals[J]. Journal of Sichuan University: Engineering Science Edition, 2004, 36(2): 94-97.
|
| [5] |
Xue D Y, Zhao C N, Chen Y Q. A modified approximation method of fractional order system[C]//IEEE International Conference on Mechatronics and Automation. Piscataway, NJ, USA: IEEE, 2006: 1043-1048.
|
| [6] |
Vinagre B M, Chen Y Q, Petras I. Two direct Tustin discretization methods for fractional-order differentiation/integrator[J]. Journal of the Franklin Institute, 2003, 340(5): 349-362.
|
| [7] |
Hamdaoui K, Charef A. A new discretization method for fractional order differentiators via the bilinear transformation[C]//Proceedings of the 15th International Conference on Digital Signal Processing. Piscataway, NJ, USA: IEEE, 2007: 280-283.
|
| [8] |
Tricaud C, Chen Y Q. An approximate method for numerically solving fractional order optimal control problems of general form[J]. Computers and Mathematics with Applications, 2010, 59(5): 1644-1655.
|
| [9] |
Charef A, Sun H, Tsao Y, et al. Fractional system as represented by singularity function[J]. IEEE Transactions on Automatic Control, 1992, 37(9): 1465-1470.
|
| [10] |
Meng L, Xue D Y. A new approximation algorithm of fractional order system models based optimization[J]. Journal of Dynamic Systems, Measurement, and Control, 2012, 134(4): 044504.
|
| [11] |
Oustaloup A, Levron F, Mathieu B, et al. Frequency-band complex noninteger differentiator: Characterization and synthesis[J]//IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications, 2000, 47(1): 25-39.
|
| [12] |
Levy E C. Complex-curve fitting[J]. IRE Transactions on Automatic Control, 1959(4): 37-44.
|
| [13] |
张启人. 大系统模型降阶理论[J]. 信息与控制, 1980, 32(4): 2-25. Zhang Q R. Model reduction theory for a large scale system[J]. Information and Control, 1980, 32(4): 2-25.
|
| [14] |
董雯彬. 分数阶线性时不变系统的降阶算法研究[D]. 沈阳: 东北大学, 2010. Dong W B. Research into the reduction algorithm for linear time invariant fractional order dynamic system[D]. Shenyang: Northeastern University, 2010.
|
| [15] |
李文, 赵慧敏. 一种分数阶微积分算子的有理函数逼近方法[J]. 自动化学报, 2011, 37(8): 999-1005. Li W, Zhao H M. Rational function approximation for fractional order differential and integral operators[J]. Acta Automatica Sinica, 2011, 37(8): 999-1005.
|
| [16] |
Santouh Z, Charef A, Assabaa M. Approximation of multiple fractional order systems[J]. Arab Research Institution Science Engineering, 2007, 3(4): 155-161.
|
| [17] |
Sun H, Onaral B. A unified approach to represent metal electrode polarization[J]. IEEE Transactions on Biomedical Engineering, 1983, 30(7): 399-406.
|
| [18] |
Li M, Lim S C, Chen S Y. Exact solution of impulse response to a class of fractional oscillators and its stability[J]. Mathematical Problems in Engineering, 2011, 2011: ID 657839.
|
| [19] |
Achar B N N, Hanneken J W, Enck T, et al. Dynamics of the fractional oscillator[J]. Physica A, 2001, 297(3/4): 361-367.
|
| [20] |
Achar B N N, Hanneken J W, Clarke T. Damping characteristics of a fractional oscillator[J]. Physica A, 2004, 339(3/4): 311-319.
|
| [21] |
Li M, Lim S C, Cattani C, et al. Characteristic roots of a class of fractional oscillators[J]. Advances in High Energy Physics, 2013, 2013: ID 853925.
|
下载:
