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

被引：26

作者：

Muthukumar, P. ^{[1
]}

Rajivganthi, C. ^{[1
]}

机构：

[1] Deemed Univ, Dept Math, Gandhigram Rural Inst, Gandhigram 624302, Tamil Nadu, India

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2013年 / 17卷 / 05期

关键词：

Approximate controllability; Fixed point theorem; Fractional order neutral stochastic integro-differential system; Hilbert space; FUNCTIONAL-DIFFERENTIAL EQUATIONS; EVOLUTION EQUATIONS; HILBERT-SPACES; MILD SOLUTIONS; BANACH-SPACES; EXISTENCE; INCLUSIONS;

D O I：

10.11650/tjm.17.2013.2743

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1693 / 1713

页数：21

共 40 条

[1] [Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892
[2] [Anonymous], 2000, Applications of Fractional Calculus in Physics
[3] [Anonymous], 1999, FRACTIONAL DIFFERENT
[4] [Anonymous], 2006, Journal of the Electrochemical Society
[5] ASTROM K. J., 1970, Introduction to stochastic control
[6] Controllability of fractional integrodifferential systems in Banach spaces
Balachandran, K.
Park, J. Y.
[J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2009, 3 (04) : 363 - 367
[7] Existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions
Balasubramaniam, P.
Park, J. Y.
Kumar, A. Vincent Antony
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (3-4) : 1049 - 1058
[8] Existence results for fractional order functional differential equations with infinite delay
Benchohra, A.
Henderson, J.
Ntouyas, S. K.
Ouahab, A.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) : 1340 - 1350
[9] Byszewski L., 1991, Applicable Analysis, V40, P11
[10] Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order
Chang, Yong-Kui
Kavitha, V.
Arjunan, M. Mallika
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (11) : 5551 - 5559

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