Controllability of nonlinear stochastic fractional higher order dynamical systems
-
R. Mabel Lizzy
,
K. Balachandran
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.
Acknowledgements
The work of first author was supported by the University Grants Commission under grant number: MANF-2015-17-TAM-50645 from the Government of India. The second author is thankful to University Grants Commission for providing the UGC-BSR Faculty Fellowship to carry out this work. The work of third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education under grant number: 2018R1D1A1B07049623.
References
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© 2019 Diogenes Co., Sofia
Articles in the same Issue
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- Editorial Note
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- Research Paper
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- Controllability of nonlinear stochastic fractional higher order dynamical systems
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Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–4–2019)
- Research Paper
- Fractional equations via convergence of forms
- About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
- Survey Paper
- The vertical slice transform on the unit sphere
- Research Paper
- Well-posedness of time-fractional advection-diffusion-reaction equations
- Existence of solutions for nonlinear fractional order p-Laplacian differential equations via critical point theory
- Exact asymptotic formulas for the heat kernels of space and time-fractional equations
- Estimates of damped fractional wave equations
- A modified time-fractional diffusion equation and its finite difference method: Regularity and error analysis
- On the fractional diffusion-advection-reaction equation in ℝ
- Controllability of nonlinear stochastic fractional higher order dynamical systems
- Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2
- Analysis of fractional order error models in adaptive systems: Mixed order cases
- Fractional calculus of variations: a novel way to look at it
- Pricing of perpetual American put option with sub-mixed fractional Brownian motion
