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Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

Abstract

In this paper we obtain the sufficient conditions for the controllability of nonlinear stochastic fractional integrodifferential systems and nonlinear systems with implicit fractional derivative in Hilbert spaces by using the fixed point technique.

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References

  1. Kilbas, A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, New York (2006)

    MATH  Google Scholar 

  2. Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University, Press (1992)

    Book  MATH  Google Scholar 

  3. Oksendal, B.: Stochastic Differential Equations: An Introduction with Applications. Springer, Heidlberg (2000)

    MATH  Google Scholar 

  4. Kamrani, M.: Numerical solution of stochastic fractional differential equations. Numer. Algorithms 68(1), 81–93 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bensoussan, A., Da Prato, G., Delfour, M.C., Mitter, S.K.: Representation and Control of Infinite Dimensional Systems. Birkhäuser, Boston (1993)

    Book  MATH  Google Scholar 

  6. Curtain, R.F., Zwart, H.: An Introduction to Infinite Dimensional Systems Theory. Springer, New York (1995)

    Book  MATH  Google Scholar 

  7. Klamka, J.: Constrained controllability of semilinear systems. Nonlinear Anal. 47, 2939–2949 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zabczyk, J.: Mathematical Control Theory. Birkhäuser, Boston (1992)

    MATH  Google Scholar 

  9. Bashirov, A.E., Mahmudov, N.I.: On concepts of controllability for linear deterministic and stochastic system. SIAM J. Control Optim. 37(6), 1808–1821 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Klamka, J.: Controllability of dynamical systems: a survey. Bull. Pol. Ac. Tech. 61(2), 221–229 (2013)

    MathSciNet  Google Scholar 

  11. Balachandran, K., Karthikeyan, S.: Controllability of nonlinear Itô stochastic integrodifferential systems. J. Franklin Inst. 345(4), 382–391 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mahmudov, N.I.: Controllability of linear stochastic systems in Hilbert spaces. J. Math. Anal. Appl. 259(1), 64–82 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mahmudov, N.I.: Controllability of semilinear stochastic systems in Hilbert spaces. J. Math. Anal. Appl. 288(1), 197–211 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Balachandran, K., Park, J.Y.: Controllability of fractional integrodifferential systems in Banach spaces. Nonlinear Anal. Hybrid Syst. 3(4), 363–367 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mabel Lizzy, R., Balachandran, K., Suvinthra, M.: Controllability of nonlinear stochastic fractional systems. J. Appl. Math. Inf. (under review)

    Google Scholar 

  16. Balachandran, K., Divya, S.: Controllability of nonlinear implicit fractional integrodifferential systems. Int. J. Appl. Math. Comput. Sci. 24(4), 713–722 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Balachandran, K., Dauer, J.P.: Controllability of nonlinear systems in Banach spaces: a survey. J. Optim. Theory Appl. 115(1), 7–28 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kreyszig, E.: Introductory Functional Analysis with Applications. Wiley, New York (1978)

    MATH  Google Scholar 

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Acknowledgments

The work was supported by the [University Grants Commission] under grant [number: MANF-2015-17-TAM-50645] from the government of India.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, India

    Rajendran Mabel Lizzy

Authors
  1. Rajendran Mabel Lizzy
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Correspondence to Rajendran Mabel Lizzy .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Lizzy, R.M. (2017). Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_31

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

  • eBook Packages: EngineeringEngineering (R0)

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