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2014 | 24 | 4 | 713-722

Tytuł artykułu

Controllability of nonlinear implicit fractional integrodifferential systems

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.

Rocznik

Tom

24

Numer

4

Strony

713-722

Opis fizyczny

Daty

wydano
2014
otrzymano
2013-11-05
poprawiono
2014-02-28

Twórcy

  • Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
  • Department of Mathematics, Bharathiar University, Coimbatore 641 046, India

Bibliografia

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  • Balachandran, K. (1988). Controllability of nonlinear systems with implicit derivatives, IMA Journal of Mathematical Control and Information 5(2): 77-83.
  • 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.
  • Balachandran, K. and Balasubramaniam, P. (1992). A note on controllability of nonlinear Volterra integrodifferential systems, Kybernetika 28(4): 284-291.
  • Balachandran, K. and Balasubramaniam, P. (1994). Controllability of nonlinear neutral Volterra integrodifferential systems, Journal of the Australian Mathematical Society 36(1): 107-116.
  • Balachandran, K. and Kokila, J. (2012a). On the controllability of fractional dynamical systems, International Journal of Applied Mathematics and Computer Science 22(3): 523-531, DOI: 10.2478/v10006-012-0039-0.
  • Balachandran, K. and Kokila, J. (2013a). Constrained controllability of fractional dynamical systems, Numerical Functional Analysis and Optimization 34(11): 1187-1205.
  • Balachandran, K. and Kokila, J. (2013b). Controllability of nonlinear implicit fractional dynamical systems, IMA Journal of Applied Mathematics 79(3): 562-570.
  • Balachandran, K., Kokila, J. and Trujillo, J.J. (2012b). Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Applications 64(10): 3037-3045.
  • Balachandran, K., Park, J.Y. and Trujillo, J.J. (2012c). Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis: Theory, Methods and Applications 75(4): 1919-1926.
  • Balachandran, K., Zhou, Y. and J. Kokila, J. (2012d). Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation 17(9): 3508-3520.
  • Burton, T.A. (1983). Volterra Integral and Differential Equations, Academic Press, New York, NY.
  • 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.
  • Dacka, C. (1980). On the controllability of a class of nonlinear systems, IEEE Transaction on Automatic Control 25(2): 263-266.
  • Kaczorek, K. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin.
  • Kexue, L. and Jigen, P. (2011). Laplace transform and fractional differential equations, Applied Mathematics Letters 24(12): 2019-2013.
  • Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
  • Klamka, J. (1975a). On the global controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(1): 170-172.
  • Klamka, J. (1975b). On the local controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(2): 289-291.
  • Klamka, J. (1975c). Controllability of nonlinear systems with delays in control, IEEE Transactions on Automatic Control AC-20(5): 702-704.
  • Klamka, J. (1993). Controllability of Dynamical Systems, Kluwer Academic, Dordrecht.
  • Klamka, J. (1999). Constrained controllability of dynamic systems, International Journal of Applied Mathematics and Computer Science 9(2): 231-244.
  • Klamka, J. (2000). Schauder's fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165.
  • Klamka, J. (2001). Constrained controllability of semilinear delayed systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(3): 505-515.
  • Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 333-337.
  • 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.
  • Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.
  • Mittal, R.C. and Nigam, R. (2008). Solution of fractional integrodifferential equations by Adomian decomposition method, International Journal of Applied Mathematics and Mechanics 4(2): 87-94.
  • Oldham, K.B and Spanier, J. (1974). The Fractional Calculus, Academic Press, London.
  • Olmstead, W.E. and Handelsman, R.A. (1976). Diffusion in a semi-infinite region with nonlinear surface dissipation, SIAM Review 18(2): 275-291.
  • Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY.
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  • Sadovskii, J.B. (1972). Linear compact and condensing operator, Russian Mathematical Surveys 27(1): 85-155.
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Typ dokumentu

Bibliografia

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bwmeta1.element.bwnjournal-article-amcv24i4p713bwm
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