Have a personal or library account? Click to login
On the controllability of fractional dynamical systems Cover

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): 021402-1-021402-5.10.1115/1.2833919
  2. Al Akaidi, M. (2008). Fractal Speech Processing, Cambridge University Press, Cambridge.
  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.
  4. Balachandran, K. and Dauer, J.P. (1987). Controllability of nonlinear systems via fixed point theorems, Journal of Optimization Theory and Applications 53(3): 345-352.10.1007/BF00938943
  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: 1-12.10.14232/ejqtde.2010.1.4
  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): 4587-4593.10.1016/j.na.2010.02.035
  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): 1970-1977.10.1016/j.cnsns.2010.08.005
  8. Balachandran, K., Park J.Y. and Trujillo, J.J. (2012). Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis: Theory, Methods & Applications 75(4): 1919-1926.10.1016/j.na.2011.09.042
  9. Benson, D.A., Wheatcraft, S.W. and Meerschaert, M.M. (2000). Application of a fractional advection-dispersion equation, Water Resources Research 36(6): 1403-1412.10.1029/2000WR900031
  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): 1531-1541.10.1177/1077546307087432
  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): 68-78.10.1016/j.amc.2006.08.104
  12. Caputo, M. (1967 ). Linear model of dissipation whose Q is almost frequency independent, Part II, Geophysical Journal of Royal Astronomical Society 13(5): 529-539.10.1111/j.1365-246X.1967.tb02303.x
  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): 2794-2802.10.1016/j.sigpro.2006.02.021
  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): 1-11.10.1615/JAutomatInfScien.v40.i6.10
  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. 233-241.10.1007/978-90-481-3293-5_19
  16. Do, V.N. (1990). Controllability of semilinear systems, Journal of Optimization Theory and Applications 65(1): 41-52.10.1007/BF00941158
  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/v10006-008-0019-6.10.2478/v10006-008-0019-6
  18. Herrmann, R. (2011). Fractional Calculus: An Introduction for Physicists, World Scientific Publishing, Singapore.10.1142/8072
  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): 253-265.10.1016/S0022-0728(71)80115-8
  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/v10006-011-0023-0.10.2478/v10006-011-0023-0
  21. Kexue, L. and Jigen, P. (2011). Laplace transform and fractional differential equations, Applied Mathematics Letters 24(12): 2019-2023.10.1016/j.aml.2011.05.035
  22. Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, New York, NY.
  23. Klamka, J. (1993). Controllability of Dynamical Systems, Kluwer Academic, Dordrecht.
  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.
  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. 503-509.10.1007/978-90-481-3293-5_45
  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): 233-245.10.1007/BF02936089
  27. Machado, J.T., Kiryakova, V. and Mainardi, F. (2011). Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulations 16(3): 1140-1153.10.1016/j.cnsns.2010.05.027
  28. Machado, J.T. (1997). Analysis and design of fractional order digital control systems, Systems Analysis, Modelling and Simulation 27(2-3): 107-122.
  29. Metzler, R. and Klafter, J. (2000). The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Physics Reports 339(1): 1-77.10.1016/S0370-1573(00)00070-3
  30. Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.
  31. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D. and Feliu, V. (2010). Fractional-order Systems and Controls: Fundamentals and Applications, Springer, London.10.1007/978-1-84996-335-0
  32. Oldham, K.B., and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
  33. Oustaloup, A. (1991). La Commade CRONE: Commande Robuste d’Ordre Non Entier, Herm`es, Paris.
  34. Podlubny, I. (1999a). Fractional Differential Equations, Academic Press, London.
  35. Podlubny, I. (1999b). Fractional-order systems and PIλDμ controllers, IEEE Transactions on Automatic Control 44(1): 208-214.10.1109/9.739144
  36. Renardy, M., Hrusa, W.J. and Nohel, J.A.(1987). Mathematical Problems in Viscoelasticity, Longman Scientific and Technical, New York, NY.
  37. Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordan and Breach, Amsterdam.
  38. Shamardan, A.B. andMoubarak, M.R.A. (1999). Controllability and observability for fractional control systems, Journal of Fractional Calculus 15(1): 25-34.
  39. Valerio, D. and Sa da Costa, J. (2004). Non integer order control of a flexible robot, Proceedings of the IFAC Workshop on Fractional Differentiation and its Applications, Bordeaux, France, pp. 520-525.
  40. West, B.J., Bologna, M. and Grigolini, P. (2003). Physics of Fractal Operators, Springer-Verlag, Berlin.10.1007/978-0-387-21746-8
DOI: https://doi.org/10.2478/v10006-012-0039-0 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
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

© 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.