Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space

Sathiyaraj T.; Balasubramaniam P.

Volume 3 Issue 4

Oct. 2016

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2016 > 3(4): 400-410

Sathiyaraj T. and Balasubramaniam P., "Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 400-410, Oct. 2016.

Citation:

Sathiyaraj T. and Balasubramaniam P., "Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 400-410, Oct. 2016.

Citation:

Sathiyaraj T. and Balasubramaniam P., "Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 400-410, Oct. 2016.

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Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space

Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram-624302, Dindigul, Tamil Nadu, India

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Council of Scientific and Industrial Research, Extramural Research Division, Pusa, New Delhi, India 25/(0217)/13/EMR-II

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Author Bio:
T. Sathiyaraj Under-graduated from Department of Mathematics, AVVM Sri Pushpam College, Poondi, Thanjavur, affiliated with Bharathidasan University, Tiruchirappalli, India, in 2008. He obtained post-graduation and Master of Philosophy from St. Joseph's College, Tiruchirappalli affiliated with Bharathidasan University in 2011 and 2012, respectively. Now, he is pursuing his Ph. D. degree under the guidance of Professor P. Balasubramaniam at Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu, India. His research interests include the analysis and control of fractional order stochastic differential equations(e-mail: sathiyaraj133@gmail.com;sathiyaraj133@gmail.com).
Corresponding author: P. Balasubramaniam Post graduated in the year 1989 and subsequently completed Master of Philosophy in the year 1990 and Doctor of Philosophy (Ph. D.) in 1994 in the field of mathematics with specialized area of control theory from Bharathiar University, Coimbatore, Tamilnadu, India. Soon after his completion of Ph. D. degree, he served as Lecturer in Mathematics in Engineering Colleges for three years. Since February 1997 he served as Lecturer and Reader in Mathematics and now he is rendering his services as a Professor, Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram, India, from November 2006 onwards. He has worked as a Visiting Research Professor during the years 2001 and 2005-2006 for promoting research in the field of control theory and neural networks at Pusan National University, Pusan, South Korea. Also he has worked as Visiting Professor in the Institute of Mathematical Sciences, University of Malaya, Malaysia, for the period of six months from September 2011 to March 2012. He is a member of several academic bodies including a life member of Cryptology Research Society of India, Indian Statistical Institute, Kolkata. He has 23 years of experience in teaching and research. He has published more than 211 research papers in various SCI journals holding impact factors with Scopus H-index 29 and web of knowledge H-Index 23. Also he has edited 7 proceedings including a book and 3 international conference proceedings in Springer publications. He is serving as a reviewer of many SCI journals and member of the editorial board of Journal of Computer Science, Advances in Fuzzy Sets and Systems and the Scientific World Journal:Mathematical Analysis, Hindawi Publisling Corporation, USA. He is an Editor-in-Chief of the journal Modern Instrumentation, Scientific Research Publishing Inc. (SCIRP) and Associate Editor of Advances in Difference Equations, Springer, Germany. He has received the Tamilnadu Scientist Award (TANSA) in the discipline of Mathematical Sciences instituted by the Tamilnadu State Council for Science and Technology in the year 2005. His research interests include the areas of control theory, stochastic differential equations, soft Computing, stability analysis, cryptography, neural networks and image processing. Corresponding author of this paper.
Received Date: 2015-08-18
Revised Date: 2016-01-13

Abstract

Abstract

In this paper, sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion (fBm) via fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case. The controllability Grammian matrix is defined by using Mittag-Leffler matrix function. Finally, a numerical example is presented to illustrate the efficiency of the obtained theoretical results.
- Controllability,
- fractional Brownian motion,
- fractional order derivatives,
- Mittag-Leffler function,
- stochastic differential inclusions

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References

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Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space

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