Controllability of nonlinear stochastic fractional higher order dynamical systems

Mabel Lizzy Rajendran; K. Balachandran; Yong-Ki Ma

doi:10.1515/fca-2019-0056

Controllability of nonlinear stochastic fractional higher order dynamical systems

Mabel Lizzy Rajendran^*, K. Balachandran, Yong-Ki Ma

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1063–1085
Number of pages	23
Journal	Fractional Calculus and Applied Analysis
Volume	22
Early online date	23 Oct 2019
DOIs	https://doi.org/10.1515/fca-2019-0056
Publication status	E-pub ahead of print - 23 Oct 2019
Externally published	Yes

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title = "Controllability of nonlinear stochastic fractional higher order dynamical systems",

abstract = "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 L{\'e}vy 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.",

author = "Rajendran, {Mabel Lizzy} and K. Balachandran and Yong-Ki Ma",

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T1 - Controllability of nonlinear stochastic fractional higher order dynamical systems

AU - Rajendran, Mabel Lizzy

AU - Balachandran, K.

AU - Ma, Yong-Ki

PY - 2019/10/23

Y1 - 2019/10/23

N2 - 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.

AB - 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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M3 - Article

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VL - 22

SP - 1063

EP - 1085

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

ER -

Controllability of nonlinear stochastic fractional higher order dynamical systems

Abstract

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