Taiwanese Journal of Mathematics

APPROXIMATE CONTROLLABILITY OF FRACTIONAL ORDER NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLOCAL CONDITIONS AND INFINITE DELAY

P. Muthukumar and C. Rajivganthi

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Abstract

This paper deals with the approximate controllability of fractional order neutral stochastic integro-differential system with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed by using the infinite dimensional controllability operator. With this control function, the sufficient conditions for approximate controllability of the proposed probelm in Hilbert space is established. Further, the results are obtained by using fractional calculus, stochastic analysis techniques, Sadovskii fixed point theorem and similar to the classical linear growth condition and the Lipschitz condition. Finally an example is provided to illustrate the application of the obtained results.

Article information

Source
Taiwanese J. Math., Volume 17, Number 5 (2013), 1693-1713.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706233

Digital Object Identifier
doi:10.11650/tjm.17.2013.2743

Mathematical Reviews number (MathSciNet)
MR3106038

Zentralblatt MATH identifier
1282.34080

Subjects
Primary: 34K50: Stochastic functional-differential equations [See also , 60Hxx] 93B05: Controllability 93E03: Stochastic systems, general

Keywords
approximate controllability fixed point theorem fractional order neutral stochastic integro-differential system Hilbert space

Citation

Muthukumar, P.; Rajivganthi, C. APPROXIMATE CONTROLLABILITY OF FRACTIONAL ORDER NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLOCAL CONDITIONS AND INFINITE DELAY. Taiwanese J. Math. 17 (2013), no. 5, 1693--1713. doi:10.11650/tjm.17.2013.2743. https://projecteuclid.org/euclid.twjm/1499706233


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