Controllability of nonlinear higher-order fractional damped stochastic systems involving multiple delays
Articles
Ganesan Arthi
PSGR Krishnammal College for Women
https://orcid.org/0000-0002-6688-4609
Kalaiselvan Suganya
PSGR Krishnammal College for Women
https://orcid.org/0000-0002-3777-518X
Juan J. Nieto
Universidade de Santiago de Compostela
https://orcid.org/0000-0001-8202-6578
Published 2022-05-24
https://doi.org/10.15388/namc.2022.27.27587
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Keywords

controllability
fractional damped systems
stochastic systems
multiple delays
Mittag-Leffler function

How to Cite

Arthi, G., Suganya, K. and Nieto, J.J. (2022) “Controllability of nonlinear higher-order fractional damped stochastic systems involving multiple delays”, Nonlinear Analysis: Modelling and Control, 27(5), pp. 879–903. doi:10.15388/namc.2022.27.27587.

Abstract

This paper is concerned with the controllability problem for higher-order fractional damped stochastic systems with multiple delays, which involves fractional Caputo derivatives of any different orders. In the process of proof, we have proposed the controllability of considered linear system by establishing a controllability Grammian matrix and employing a control function. Sufficient conditions for the considered nonlinear system concerned to be controllable have been derived by constructing a proper control function and utilizing the Banach fixed point theorem with Burkholder–Davis–Gundy’s inequality. Finally, two examples are provided to emphasize the applicability of the derived results.

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