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Author: search.filters.author.Arthi G

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    ON FINITE-TIME STABILITY OF NONLINEAR FRACTIONAL-ORDER SYSTEMS WITH IMPULSES AND MULTI-STATE TIME DELAYS
    (Elsevier, 2021-04) Arthi G; Brindha N
    This work concentrates on the finite-time stability (FTS) analysis of fractional-order systems (FOS) with impulsive effects and multi-state time delays. The condition which give assurance for FTS of nonlinear FOS having impulsive behavior and multi-state time delay are derived by utilizing the generalization of Gronwall’s inequality (GI). At last, two numerical examples are given which provide the accuracy of the given result.
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    CONTROLLABILITY OF NON-LINEAR FRACTIONAL-ORDER SYSTEMS WITH DAMPING BEHAVIOUR AND MULTIPLE DELAYS
    (Oxford Academic, 2021-09) Arthi G; Suganya K
    A controllability analysis of both linear and non-linear fractional-order systems with damping behaviour and multiple delays is studied. We derived the controllability result for damped system with multi-term fractional order and multiple delays by introducing some lemmas with the help of Laplace transform properties and Mittag–Leffler function. Further, some new sufficient conditions ensuring controllability for a class of non-linear multi-term fractional-order damped systems with multiple delays are established by utilizing fractional Caputo derivatives and Schauder’s fixed point theorem. Moreover, as applications that demonstrate the proposed results, two examples are presented.
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    CONTROLLABILITY OF HIGHER ORDER STOCHASTIC FRACTIONAL CONTROL DELAY SYSTEMS INVOLVING DAMPING BEHAVIOR
    (Elsevier, 2021-12-01) Arthi G; Suganya K
    This article focuses on the problem of controllability of both cases linear and nonlinear higher order stochastic fractional control delay systems with damping behavior, which involving Caputo fractional derivative (CFD). The proposed approach utilizes the ideas of controllability Grammian matrix involving Mittag-Leffler function (MLF) and Burkholder-Davis-Gundy’s inequality. By employing Banach fixed point theorem, we establish the exact method to design a stochastic perturbation to control the considered nonlinear higher order fractional differential systems. As a final point, the derived design is illustrated with two numerical examples.
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    APPROXIMATE CONTROLLABILITY OF NONLINEAR FRACTIONAL STOCHASTIC SYSTEMS INVOLVING IMPULSIVE EFFECTS AND STATE DEPENDENT DELAY
    (Universal Wiser Publisher, 2023-06-17) Arthi G; Suriyapriya N
    This paper studies the analysis of approximate controllability for the fractional order neutral stochastic impulsive integro-differential systems involving nonlocal condition and State Dependent Delay (SDD). Sufficient conditions are designed to illustrate the evaluation of approximate controllability. It is exhibited that the proposed protocol can explicitly drive the results by Krasnoselskii's fixed point technique and semigroup theory. As a final point, the derived scheme is validated through an example.