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On the controllability of fractional dynamical systems Cover

On the controllability of fractional dynamical systems

International Journal of Applied Mathematics and Computer Science
Volume 22 (2012): Issue 3 (September 2012)
By:  and    
Open Access
|Sep 2012
References

References

  1. Adams, J.L. and Hartley, T.T. (2008). Finite time controllability of fractional order systems, Journal of Computational and Nonlinear Dynamics 3(2): 021402-1-021402-5.
    Open DOISearch in Google Scholar
  2. Al Akaidi, M. (2008). Fractal Speech Processing, Cambridge University Press, Cambridge.
    Search in Google Scholar
  3. Arena, P., Caponetta, R., Fortuna L. and Porto, D. (2008). Nonlinear Noninteger Order Circuits and Systems: An Introduction, World Scientific Series on Nonlinear Science, Vol. 38, World Scientific, Singapore.
    Search in Google Scholar
  4. Balachandran, K. and Dauer, J.P. (1987). Controllability of nonlinear systems via fixed point theorems, Journal of Optimization Theory and Applications 53(3): 345-352.
    Open DOISearch in Google Scholar
  5. Balachandran, K. and Kiruthika, S. (2010). Existence of solutions of abstract fractional impulsive semilinear evolution equations, Electronic Journal of Qualitative Theory of Differential Equations 4: 1-12.
    Open DOISearch in Google Scholar
  6. Balachandran, K. and Trujillo, J.J. (2010). The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Analysis: Theory, Methods and Applications 72(12): 4587-4593.
    Open DOISearch in Google Scholar
  7. Balachandran, K., Kiruthika, S. and Trujillo, J.J. (2011). Existence results for fractional impulsive integrodifferential equations in Banach spaces, Communication in Nonlinear Science and Numerical Simulation 16(4): 1970-1977.
    Open DOISearch in Google Scholar
  8. Balachandran, K., Park J.Y. and Trujillo, J.J. (2012). Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis: Theory, Methods & Applications 75(4): 1919-1926.
    Open DOISearch in Google Scholar
  9. Benson, D.A., Wheatcraft, S.W. and Meerschaert, M.M. (2000). Application of a fractional advection-dispersion equation, Water Resources Research 36(6): 1403-1412.
    Open DOISearch in Google Scholar
  10. Bettayeb, M. and Djennoune, S. (2008). New results on the controllability and observability of fractional dynamical systems, Journal of Vibrating and Control 14(9-10): 1531-1541.
    Open DOISearch in Google Scholar
  11. Bonilla, B., Rivero, M. and Trujillo, J.J. (2007). On systems of linear fractional differential equations with constant coefficients, Applied Mathematics and Computation 187(1): 68-78.
    Open DOISearch in Google Scholar
  12. Caputo, M. (1967 ). Linear model of dissipation whose Q is almost frequency independent, Part II, Geophysical Journal of Royal Astronomical Society 13(5): 529-539.
    Open DOISearch in Google Scholar
  13. Chen, Y.Q., Ahn, H.S. and Xue, D. (2006). Robust controllability of interval fractional order linear time invariant systems, Signal Processing 86(10): 2794-2802.
    Open DOISearch in Google Scholar
  14. Chikrii, A.A. and Matichin, I.I. (2008). Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann-Liouville, Caputo and Miller-Ross, Journal of Automation and Information Sciences 40(6): 1-11.
    Open DOISearch in Google Scholar
  15. Chikrii, A. and Matichin, I.I. (2010). Game problems for fractional order systems, in D. Baleanu, Z.B. Guvenc and J.A.T. Machado (Eds.), New Trends in Nanotechnology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 233-241.
    Open DOISearch in Google Scholar
  16. Do, V.N. (1990). Controllability of semilinear systems, Journal of Optimization Theory and Applications 65(1): 41-52.
    Open DOISearch in Google Scholar
  17. Guermah, S.A., Djennoune, S.A. and Bettayeb, M.A.(2008). Controllability and observability of linear discrete time fractional order systems, International Journal of Applied Mathematics and Computer Science 18(2): 213-222, DOI: 10.2478/v10006-008-0019-6.
    Open DOISearch in Google Scholar
  18. Herrmann, R. (2011). Fractional Calculus: An Introduction for Physicists, World Scientific Publishing, Singapore.
    Open DOISearch in Google Scholar
  19. Ichise, M., Nagayanagi, Y. and Kojima, T. (1971). Analog simulation of non integer order transfer functions for analysis of electrode processes, Journal of Electroanalytical Chemistry 33(2): 253-265.
    Open DOISearch in Google Scholar
  20. Karthikeyan, S. and Balachandran, K. (2011). Constrained controllability of nonlinear stochastic impulsive systems, International Journal of Applied Mathematics and Computer Science 21(2): 307-316, DOI: 10.2478/v10006-011-0023-0.
    Open DOISearch in Google Scholar
  21. Kexue, L. and Jigen, P. (2011). Laplace transform and fractional differential equations, Applied Mathematics Letters 24(12): 2019-2023.
    Open DOISearch in Google Scholar
  22. Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, New York, NY.
    Search in Google Scholar
  23. Klamka, J. (1993). Controllability of Dynamical Systems, Kluwer Academic, Dordrecht.
    Search in Google Scholar
  24. Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 333-337.
    Search in Google Scholar
  25. Klamka, J. (2010). Controllability and minimum energy control problem of fractional discrete time systems, in D. Baleanu, Z.B. Guvenc and J.A.T. Machado (Eds.), New Trends in Nanotechnology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509.
    Open DOISearch in Google Scholar
  26. Liu, F., Anh, V.V., Turner, I. and Zhuang, P. (2003). Time fractional advection-dispersion equation, Journal of Applied Mathematics and Computing 13(1-2): 233-245.
    Open DOISearch in Google Scholar
  27. Machado, J.T., Kiryakova, V. and Mainardi, F. (2011). Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulations 16(3): 1140-1153.
    Open DOISearch in Google Scholar
  28. Machado, J.T. (1997). Analysis and design of fractional order digital control systems,(2-3): 107-122.
    Search in Google Scholar
  29. Metzler, R. and Klafter, J. (2000). The random walk’s guide to anomalous diffusion: A fractional dynamics approach,(1): 1-77.
    Open DOISearch in Google Scholar
  30. Miller, K.S. and Ross, B. (1993)., Wiley, New York, NY.
    Search in Google Scholar
  31. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D. and Feliu, V. (2010)., Springer, London.
    Open DOISearch in Google Scholar
  32. Oldham, K.B., and Spanier, J. (1974)., Academic Press, New York, NY.
    Search in Google Scholar
  33. Oustaloup, A. (1991)., Herm`es, Paris.
    Search in Google Scholar
  34. Podlubny, I. (1999a)., Academic Press, London.
    Search in Google Scholar
  35. Podlubny, I. (1999b). Fractional-order systems andcontrollers,(1): 208-214.
    Open DOISearch in Google Scholar
  36. Renardy, M., Hrusa, W.J. and Nohel, J.A.(1987)., Longman Scientific and Technical, New York, NY.
    Search in Google Scholar
  37. Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993)., Gordan and Breach, Amsterdam.
    Search in Google Scholar
  38. Shamardan, A.B. andMoubarak, M.R.A. (1999). Controllability and observability for fractional control systems,(1): 25-34.
    Search in Google Scholar
  39. Valerio, D. and Sa da Costa, J. (2004). Non integer order control of a flexible robot,, pp. 520-525.
    Search in Google Scholar
  40. West, B.J., Bologna, M. and Grigolini, P. (2003)., Springer-Verlag, Berlin.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/v10006-012-0039-0 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
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Language: English
Page range: 523 - 531
Published on: Sep 28, 2012
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
controllability,
fractional differential equations,
Mittag-Leffler function
Related subjects:
Mathematics,
Applied mathematics

© 2012 Krishnan Balachandran, Jayakumar Kokila, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 22 (2012): Issue 3 (September 2012)
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