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Approximate Controllability of Impulsive Neutral Functional Differential Equations with State-dependent Delay via Fractional Operators

by N. Y. Nadaf, M. Mallika Arjunan
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 69 - Number 2
Year of Publication: 2013
Authors: N. Y. Nadaf, M. Mallika Arjunan
10.5120/11811-7479

N. Y. Nadaf, M. Mallika Arjunan . Approximate Controllability of Impulsive Neutral Functional Differential Equations with State-dependent Delay via Fractional Operators. International Journal of Computer Applications. 69, 2 ( May 2013), 1-8. DOI=10.5120/11811-7479

@article{ 10.5120/11811-7479,
author = { N. Y. Nadaf, M. Mallika Arjunan },
title = { Approximate Controllability of Impulsive Neutral Functional Differential Equations with State-dependent Delay via Fractional Operators },
journal = { International Journal of Computer Applications },
issue_date = { May 2013 },
volume = { 69 },
number = { 2 },
month = { May },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume69/number2/11811-7479/ },
doi = { 10.5120/11811-7479 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:29:09.366765+05:30
%A N. Y. Nadaf
%A M. Mallika Arjunan
%T Approximate Controllability of Impulsive Neutral Functional Differential Equations with State-dependent Delay via Fractional Operators
%J International Journal of Computer Applications
%@ 0975-8887
%V 69
%N 2
%P 1-8
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this article, the problem of approximate controllability for nonlinear impulsive neutral differential systems with state-dependent delay is studied under the assumption that the corresponding linear control system is approximately controllable. Using Schauder's fixed point theorem and fractional powers of operators with semigroup theory, sufficient conditions are formulated and proved.

References
  1. Y. V. Rogovchenko, Impulsive evolution systems: Main results and new trends, Dynam. Contin. ,Discrete Impuls. Systems, 3 (1997), 57-88.
  2. M. Benchohra, J. Henderson and S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Series Contemporary Mathematics and Its Applications, Vol. 2, Hindawi Publ. Corp. ,2006.
  3. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific Pub. Co. , Singapore, 1989.
  4. A. Samoilenko and N. Peresyuk, Differential Equations with Impusive Effectes, World Scientific Pub. Co. , Singapore, 1995.
  5. M. Benchohra, A. Ouahab, Controllability results for functional semilinear differential inclusions in Frechet spaces, Nonlinear Anal. TMA, 61(2005), 405-423.
  6. N. Abada, M. Benchohra and H. Hammouche, Existence and controllability results for nondensely dened impulsive semilinear functional differential inclusions, J. Differ. Equ. , 246 (2009), 3834-3863.
  7. J. Klamka, Constrained controllability of semilinear systems with delays, Nonlinear Dynam. , 56 (2009), 169-177.
  8. J. Klamka, Constrained controllability of semilinear systems with delayed controls, Bull. Pol. Ac. Tech. , 56 (2008), 333-337.
  9. L. Gorniewicz, S. K. Ntouyasand D. O'Regan, Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces, Rep. Math. Phys. , 56 (2005), 437-470.
  10. L. Gorniewicz, S. K. Ntouyas and D. O'Regan, Existence and controllability results for first and second order functional semilinear differential inclusions with nonlocal conditions, Numer. Funct. Anal. Optim. , 28 (2007), 53-82.
  11. L. Gorniewicz, S. K. Ntouyas, D. O'Regan, Controllability results for -rst and second order evolution inclusions with nonlocal conditions, Ann. Polon. Math. , 89 (2006), 65-101.
  12. N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal Conditions, Nonlinear Anal. TMA, 68 (2008), 536-546.
  13. R. Sakthivel, Y. Ren and N. I. Mahmudov, Approximate controllability of second order stochastic differential equations with impulsive e-ects, Modern Phys. Lett. B 24 (2010), 1559-1572.
  14. R. Sakthivel, J. Juan, Nieto, N. I. Mahmudov, Approximate controllability of nonlinear deterministic and stochastic systems with unbounded delay, Taiwan J. Math. , 14 (2010), 1777-1797.
  15. R. Sakthivel, Approximate controllability of impulsive stochastic evolution Equations, Funkcialaj Ekvacioj, 52 (2009), 381-393.
  16. J. Klamka, Constrained approximate controllability, IEEE. T. Automat. Contr. , 45 (2000), 1745-1749.
  17. R. Sakthivel and E. R. Anandhi, Approximate controllability of impulsive differential equations with statedependent delay, International Journal of Control, 82, 2 (2010), 387-393.
  18. B. Radhakrishnan and K. Balachandran, Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay, Nonlinear Analysis, HS, 5 (2011), 655-670.
  19. N. I. Mahmudov, Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces, SIAM J, Control Optim. , 42 (2003), 1604-1622.
  20. Y. -K. Chang and W. S. Li, Solvability for impulsive neutral integrodifferential equations with statedependent delay via fractional operators, J. Optim. Theory Appl. , 144 (2010), 445-459.
  21. M. Mallika Arjunan and V. Kavitha, Existence results for impulsive neutral functional differential equations with state-dependent delay, Electronic Journal of Qualitative Theory of Differential equations, 26 (2009), 1-13.
  22. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, (1983).
  23. Y. Heno, S. Murakami and T. Naito, Functional differential equations with infinite delay, Lecturer Notes in Mathematics, 1473, Springer-Verlag, Berlin, 1991.
  24. E. Hernandez, R. Sakthivel and S. Tanaka, Existence results for impulsive evolution equations with statedependent delay, Electro. J. Differential Equations, 28 (2008), 1-11.
  25. A. E. Bashirov and N. I. Mahmudov, On concept of controllability for linear deterministic and stochastic systems, SIAM, J. Control Optim. , 37 (1999), 1808- 1821.
  26. E. Hernandez, A. Prokopczyk and L. A. Ladeira, A note on partial functional differential equations with state-dependent delay, Nonlinear Anal. RWA, 7 (2006), 510-519.
  27. A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, 2003.
Index Terms

Computer Science
Information Sciences

Keywords

Approximate controllability Impulsive neutral functional differential equations Semigroup theory State-dependent delay Fixed point

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