CONTROLLABILITY RESULTS FOR NONLINEAR IMPULSIVE FUZZY NEUTRAL INTEGRODIFFERENTIAL EVOLUTION SYSTEMS

B. Radhakrishan, P. Anukokila, T. Sathya

IJPAM: Volume 114, No. 1 (2017)

Title

CONTROLLABILITY RESULTS FOR NONLINEAR IMPULSIVE
FUZZY NEUTRAL INTEGRODIFFERENTIAL
EVOLUTION SYSTEMS

Authors

B. Radhakrishan

, P. Anukokila

, T. Sathya

$^{1,3}$ Department of Mathematics
PSG College of Technology
Coimbatore, 641004, TN, INDIA

Department of Mathematics
PSG College of Arts and Science
Coimbatore, 641014, TN, INDIA

Abstract

In this paper, author's studied the controllability results for nonlinear fuzzy neutral integrodifferential systems. Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous, and compactly supported interval fuzzy number. The results are obtained by using the Banach fixed point theorem and evolution family of functions.

History

Received: July 13, 2016
Revised: February 20, 2017
Published: April 21, 2017

AMS Classification, Key Words

AMS Subject Classification: 93B05, 03E72, 47H10, 34K40
Key Words and Phrases: controllability, fuzzy set, fuzzy number, neutral integrodifferential system, fuzzy solution, fixed point theorem

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Bibliography

1: R. Alikhani, F. Bahrami, A. Jabbari, Existence of global solutions to nonlinear Fuzzy Volterra Integrodifferential Equations, Nonlinear Anal.Theory Methods Appl., 75 (2012), 1810-1821.
2: R.J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12.
3: K. Balachandran, J. P. Duar, Existence of solutions of perturbed fuzzy integral equations in Banach spaces, Indian J. pure Appl. Math., 21 (1997), 1461-1468.
4: L. Byszewski; Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), 494-505.
5: P. Diamand, P.E. Kloeden, Metric Space of Fuzzy Sets, World Scientific, (1994).
6: D. Dubois, H. Prade, Towards fuzzy differential calculus. Part 1: Integration of fuzzy mappings, Fuzzy Sets Sys., 8 (1982), 1-17.
7: D. Dubois, H. Prade, Towards fuzzy differential calculus. Part 2: Integration on fuzzy intervals, Fuzzy Sets Sys., 8 (1982), 105-116.
8: D. Dubois, H. Prade, Towards fuzzy differential calculus. Part 3: Differentiation, Fuzzy Sets Sys., 8 (1982), 225-233.
9: Z. Ding, A. Kandel, On the controllability of fuzzy dynamical systems (I), J.Fuzzy Math., 8 (2000), 203-214.
10: D. Guo, X. Liu, Extremal solutions of nonlinear impulsive integrodifferential equations in Banach spaces, J. Math. Anal. Appl., 177 (1993), 538-552.
11: J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Springer-Verlag, New York, 1993.
12: E.Hernandez, M.Rabello and H.R.Henriquez, Existence of solutions for impulsive partial neutral functional differential equations, J.Math.Anal.Appl., 331 (2007), 1135-1158.
13: O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
14: Y.C. Kwun, D.G. Park, Optimal control problem for fuzzy differentiations, Proceedings of the Korea-Vietnam Joint Seminar., (1998), 103-114.
15: Y. Lin and J.H. Liu; Semilinear integrodifferential equations with nonlocal Cauchy problem, J. Integral Equa. Appl., 15 (2003), 79-93.
16: M. Mizumpto, K. Tanaka, Some properties of Fuzzy Numbers, North Holland (2004).
17: M.L. Puri, D.A. Ralescu, Differentials for fuzzy functions, J.Math.Anal. Appl., 91 (1983), 552-558.
18: M.L. Puri, D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl., 114 (1986), 409-422.
19: B. Radhakrishnan, K. Balachandran; Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions, J. Control Theory Appl., 10 (2012), 28-34.
20: A. M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
21: S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets Sys., 24 (1987), 319-330.
22: H. J. Zimmermann, Fuzzy Sets Decision - Making and Expert Systems,Kluwar Academic Publisher, Boston, (1987).

How to Cite?

DOI: 10.12732/ijpam.v114i1.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 114
Issue: 1
Pages: 61 - 76

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