A note on fractional-order derivatives of periodic functions

Automatica

Volumn 46, Issue 5, 2010, Pages 945-948

  Tavazoei, Mohammad Saleh ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fractional calculus; Fractional order derivative; Fractional order system; Periodic solution

Indexed keywords

FRACTIONAL CALCULUS; FRACTIONAL-ORDER SYSTEMS; NON-EXISTENCE; PERIODIC FUNCTION; PERIODIC RESPONSE; PERIODIC SOLUTION; SOLUTION ANALYSIS;

CALCULATIONS;

PROBLEM SOLVING;

EID: 77950629871     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.02.023     Document Type: Article

References (20)

1. Aoun M., Malti R., Levron F., and Oustaloup A. Synthesis of fractional Laguerre basis for system approximation. Automatica 43 (2007) 1640-1648
2. Diethelm K., and Ford N.J. Multi-order fractional differential equations and their numerical solution. Applied Mathematics and Computation 154 (2004) 621-640
3. + T-cells. Mathematical and Computer Modelling 50 (2009) 386-392
4. Edwards J.T., Ford N.J., and Simpson A.C. The numerical solution of linear multi-term fractional differential equations: systems of equations. Journal of Computational and Applied Mathematics 148 (2002) 401-418
5. Feliu-Batlle V., Rivas Pérez R., Castillo García F.J., and Sanchez Rodriguez L. Smith predictor based robust fractional-order control: application to water distribution in a main irrigation canal pool. Journal of Process Control 19 3 (2009) 506-519
6. Fitt A.D., Goodwin A.R.H., Ronaldson K.A., and Wakeham W.A. A fractional differential equation for a MEMS viscometer used in the oil industry. Journal of Computational and Applied Mathematics 229 (2009) 373-381
7. Hartley T.T., and Lorenzo C.F. Fractional-order system identification based on continuous order-distributions. Signal Processing 83 (2003) 2287-2300
8. Li Y., Chen Y.Q., and Podlubny I. Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45 (2009) 1965-1969
9. Li C., and Deng W. Remarks on fractional derivatives. Applied Mathematics and Computation 187 (2007) 777-784
10. Monje C.A., Vinagre B.M., Feliu V., and Chen Y.Q. Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice 16 (2008) 798-812
11. Nimmo S., and Evans A.K. The effects of continuously varying the fractional differential order of a chaotic nonlinear system. Chaos, Solitons and Fractals 10 (1999) 1111-1118
12. Oldham K.B. Fractional differential equations in electrochemistry. Advances in Engineering Software 41 (2010) 9-12
13. Podlubny I. Fractional differential equations (1999), Academic Press, San Diego
14. Poinot T., and Trigeassou J.C. Identification of fractional systems using an output-error technique. Nonlinear Dynamics 38 (2004) 133-154
15. Reyes-Melo M.E., González-González V.A., Guerrero-Salazar C.A., García-Cavazos F., and Ortiz-Méndez U. Application of fractional calculus to the modeling of the complex rheological behavior of polymers: from the glass transition to flow behavior. I. The theoretical model. Journal of Applied Polymer Science 108 2 (2008) 731-737
16. Tavazoei M.S., and Haeri M. A proof for non existence of periodic solutions in time invariant fractional order systems. Automatica 45 (2009) 1886-1890
17. Tavazoei M.S., and Haeri M. Describing function based methods for predicting chaos in a class of fractional order differential equations. Nonlinear Dynamics 57 (2009) 363-373
18. Tavazoei M.S., Haeri M., Attari M., Bolouki S., and Siami M. More details on analysis of fractional-order van der pol oscillator. Journal of Vibration and Control 15 6 (2009) 803-819
19. Tavazoei M.S., Haeri M., Jafari S., Bolouki S., and Siami M. Some applications of fractional calculus in suppression of chaotic oscillations. IEEE Transactions on Industrial Electronics 11 (2008) 4094-4101
20. Tavazoei M.S., Haeri M., and Nazari N. Analysis of undamped oscillations generated by marginally stable fractional order systems. Signal Processing 88 (2008) 2971-2978