Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces

Rajendran, Mabel Lizzy

doi:10.1007/978-3-319-45474-0_31

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…Assumption A 1 [15]: For solution representation of the system (3.1), we consider this assumption. The operator A ∈ L(Y ) commutes with the fractional integral operator I α on Y and…”

Section: Resultsmentioning

confidence: 99%

“…Lemma 2.1. [15] Suppose that A is a bounded linear operator defined on a Banach space, and assume that ∥A∥ < 1. Then (I − A) −1 is linear and bounded.…”

Section: Fractional Calculusmentioning

confidence: 99%

“…It has huge applications in various research areas, including environment, finance, and medicine, etc. For important works of fractional stochastic systems and their applications, we may refer to [15,18,19,23,25].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Fractional Order Neutral-Type Stochastic Integro-Differential System With Rosenblatt Process - A Controllability Exploration

2022

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan

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We investigate the controllability analysis of nonlinear fractional order neutral-type stochastic integro-differential system with non-Gaussian process. We stress out the stochastic term of our system driven by the uncomplicated non-Gaussian Hermite process known as the Rosenblatt process, which is named after by Murray Rosenblatt who first devised this introduced concept. This process is self-similar with consistent accretion and beside emerged as restriction in the non-central limit theorem, and it exists in the second wiener chaos. The necessary and sufficient conditions for the controllability are verified by employing fixed point techniques. At end, we present illustrative examples to clarify the abstract results.

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“…Assumption A 1 [15]: For solution representation of the system (3.1), we consider this assumption. The operator A ∈ L(Y ) commutes with the fractional integral operator I α on Y and…”

Section: Resultsmentioning

confidence: 99%

“…Lemma 2.1. [15] Suppose that A is a bounded linear operator defined on a Banach space, and assume that ∥A∥ < 1. Then (I − A) −1 is linear and bounded.…”

Section: Fractional Calculusmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Fractional Order Neutral-Type Stochastic Integro-Differential System With Rosenblatt Process - A Controllability Exploration

2022

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan

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Controllability of Nonlinear Stochastic Fractional Higher Order Dynamical Systems

Lizzy

Balachandran

2019

FCAA

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This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

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Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces

Cited by 2 publications

References 12 publications

Nonlinear Fractional Order Neutral-Type Stochastic Integro-Differential System With Rosenblatt Process - A Controllability Exploration

Nonlinear Fractional Order Neutral-Type Stochastic Integro-Differential System With Rosenblatt Process - A Controllability Exploration

Controllability of Nonlinear Stochastic Fractional Higher Order Dynamical Systems

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