a) 2024-Scopus Open Access (pdf)

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CONTROLLABILITY OF IMPULSIVE DAMPED FRACTIONAL ORDER SYSTEMS INVOLVING STATE DEPENDENT DELAY (Article)
(Universal Wiser Publisher, 2024) Arthi, G; Vaanmathi, M
In this article, the concept of controllability on fractional order impulsive systems involving state dependent delay and damping behavior is analysed by utilizing Caputo fractional derivative. The main motivation is to derive the sufficient conditions for the controllability of the considered systems. Based on the Laplace transform and inverse Laplace transform, the solution of fractional-order dynamical systems are obtained. The results are established by utilizing basic ideas of fractional calculus, Mittag-Leffler function and Banach fixed point theorem. Finally, an application is provided to illustrate the derived result.
CONTROLLABILITY OF STOCHASTIC FRACTIONAL SYSTEMS INVOLVING STATE-DEPENDENT DELAY AND IMPULSIVE EFFECTS (Article)
(Springer Science and Business Media Deutschland GmbH, 2024) Arthi, G; Vaanmathi, M; Ma, Yong-Ki
In this paper, the controllability concept of a nonlinear fractional stochastic system involving state-dependent delay and impulsive effects is addressed by employing Caputo derivatives and Mittag-Leffler (ML) functions. Based on stochastic analysis theory, novel sufficient conditions are derived for the considered nonlinear system by utilizing Krasnoselkii’s fixed point theorem. Correspondingly, the applicability of the derived theoretical results is indicated by an example