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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Approximate Controllability of Impulsive Neutral Functional Integrodifferential Systems with Nonlocal Conditions

Discontinuity, Nonlinearity, and Complexity 7(4) (2018) 451--462 | DOI:10.5890/DNC.2018.12.009

A. Yasotha$^{1}$, K. Kanagarajan$^{2}$

$^{1}$ Department of Mathematics, United Institute of Technology, Coimbatore, India

$^{2}$ Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India

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Abstract

In this paper, we study the approximate controllability of impulsive neutral functional integrodifferential systems with finite delay. The fractional power theory and a-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability of the impulsive integrodifferential equation are formulated and proved. An example is provided to illustrate the theory.

References

  1. [1]  Ballinger, G. and Liu, X. (2003), Boundedness for impulsive delay differential equations and applications to population growth modes, Nonlinear Analysis, 53, 1041-1062.
  2. [2]  Yang, T. (2001), Impulsive systems and control: Theory and Applications, Springer-Verlag, Berlin.
  3. [3]  Abada, N., Benchohra, M., and Hammouche, H. (2009), Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, Journal of Differential Equations, 246, 3834-3863.
  4. [4]  Chang, Y.K. (2007), Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos Solitons Fractals, 33, 1601-1609.
  5. [5]  Fu, X. and Mei, K. (2009), Approximate controllability of semilinear partial functional differential systems, Journal of Dynamical and Control Systems, 15 , 425 - 443.
  6. [6]  Dauer, J.P. and Mahmudov, N.I. (2002), Approximate controllability of semilinear functional equations in Hilbert spaces, Journal of Mathematical Analysis and Applications, 273, 310-327.
  7. [7]  Do, V.N. (1989), A Note on approximate controllability of semilinear systems, Systems Control Letters, 12, 365-371.
  8. [8]  Fu, X. andRong, H. (2016), Approximate controllability of semilinear non-autonomous evolutionary systems with nonlocal conditions, Automation and Remote Control, 77, 428 - 442.
  9. [9]  George, R.J. (1995) Approximate controllability of non-autonomous Semilinear Systems, Nonlinear Analysis, 24, 1377-1393.
  10. [10]  Naito, K. (1987), Controllability of semilinear control systems dominated by the linear part, SIAM Journal of Control Optimization, 25, 715-722.
  11. [11]  Radhakrishnan, B. and Balachandran, K. (2011), Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay, Nonlinear Analysis: Hybrid Systems, 5, 655-670.
  12. [12]  Subalakshmi, R. and Banachandran, K. (2009), Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces, Chaos Solitons Fractals, 42, 2035-2046.
  13. [13]  Li, M.L., Wang, M.S., and Zhang, F.Q. (2006), Controllability of impulsive functional differential systems in Banach spaces, Chaos Solitons Fractals, 29, 175-181.
  14. [14]  Sakthivel, R., Mahmudov, N.I., and Kim, J.H. (2007), Approximate controllability of nonlinear impulsive differential systems, Reports on Mathematical Physics, 60, 85-96.
  15. [15]  Zhou, H.X. (1983), Approximate controllability for a class of semilinear abstract equations, SIAM Journal of Control Optimization, 21, 551-565.
  16. [16]  Fu, X. and Zhang, J. (2016), Approximate controllability of neutral functional differential systems with state-dependent delay, Chinese Annals of Mathematics: Series B, 37, 291-308.
  17. [17]  Arora, U. and Sukavanam, N. (2015), Approximate controllability of second order semilinear stochastic system with nonlocal conditions, Applied Mathematics and Computation, 258, 111-119.
  18. [18]  Das, S., Pandey, D., and Sukuvanam, N. (2016), Existence of solution and approximate controllability of a secondorder neutral stochastic differential equation with state dependent delay, Acta Mathematica Scientia, 36, 1509-1523.
  19. [19]  Mokkedem, F.Z. and Fu, X. (2014), Approximate controllability of semi-linear neutral integrodifferential systems with finite delay, Applied Mathematics and Computation, 242, 202-215.
  20. [20]  Pazy, A. (1983), Semigroup of linear operators and applications to partial differential equations, Springer-Verlag, New York.
  21. [21]  Sadovskii, B.N. (1967), On a Fixed point principle, Functional Analysis and Applications, 1, 74-76.