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Boundary controllability of nonlinear stochastic fractional systems in Hilbert spaces

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EN
Abstrakty
EN
Sufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.
Twórcy
  • Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
  • Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
Bibliografia
  • [1] Balachandran, K. and Anandhi, E.R. (2001). Boundary controllability of integrodifferential systems in Banach spaces, Proceedings of the Indian Academy of Sciences (Mathematical Sciences) 111(1): 127–135, DOI: 10.1007/BF02829544.
  • [2] Balachandran, K. and Divya, S. (2014). Controllability of nonlinear implicit fractional integrodifferential systems, International Journal of Applied Mathematics and Computer Science 24(4): 713–722, DOI: 10.2478/amcs-2014-0052.
  • [3] Balachandran, K. and Kokila, J. (2012). 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.
  • [4] Balachandran, K., Matar, M. and Trujillo, J.J. (2016). Note on controllability of linear fractional dynamical systems, Journal of Control and Decision 3(4): 267–279, DOI: 10.1080/23307706.2016.1217754.
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  • [7] Bashirov, A.E. (2003). Partially Observable Linear Systems under Dependent Noises, Springer, Boston, MA.
  • [8] Curtain, R.F. and Zwart, H. (1995). An Introduction to Infinite Dimensional Systems Theory, Springer-Verlag, New York, NY.
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  • [21] Mabel Lizzy, R., Balachandran, K. and Suvinthra, M. (2017). Controllability of nonlinear stochastic fractional systems with distributed delays in control, Journal of Control and Decision 4(3): 153–167, DOI: 10.1080/23307706.2017.1297690.
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  • [23] Mahmudov, N.I. (2003). Controllability of semilinear stochastic systems in Hilbert spaces, Journal of Mathematical Analysis and Applications 288(1): 197–211.
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  • [25] Oprzędkiewicz, K., Gawin, E. and Mitkowski, W. (2016). Modelling heat distribution with the use of a non-integer order, state space model, International Journal of Applied Mathematics and Computer Science 26(4): 749–756, DOI: 10.1515/amcs-2016-0052.
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Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1874bd9b-06ff-498a-9801-30374ced829b
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