Fractional Langevin type equations for white noise distributions
-
Un Cig Ji
,
Mi Ra Lee
Abstract
In this paper, by applying the intertwining properties, we introduce the fractional powers of the number operator perturbed by generalized Gross Laplacians (infinite dimensional Laplacians), which are special types of the infinitesimal generators of generalized Mehler semigroups. By applying the intertwining properties and semigroup approach, we study the Langevin type equations associated with the infinite dimensional Laplacians and with white noise distributions as forcing terms. Then we investigate the unique solution of the fractional Langevin type equations associated with the Riemann-Liouville and Caputo time fractional derivatives, and the fractional power of the infinite dimensional Laplacians, for which we apply the intertwining properties again. For our purpose, we discuss the fractional integrals and fractional derivatives of white noise distribution valued functions.
Acknowledgements
This work is supported by Basic Science Research Program through the NSF funded by the MEST (NRF-2016R1D1A1B01008782).
References
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© 2021 Diogenes Co., Sofia
Articles in the same Issue
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- Research Paper
- Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
- Tutorial paper
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- The rate of convergence on fractional power dissipative operator on compact manifolds
- Fractional Langevin type equations for white noise distributions
- Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
- Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
- The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
- Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
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Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–4–2021)
- Research Paper
- Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
- Tutorial paper
- The bouncing ball and the Grünwald-Letnikov definition of fractional derivative
- Research Paper
- Fractional diffusion-wave equations: Hidden regularity for weak solutions
- Censored stable subordinators and fractional derivatives
- Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem
- Multivariable fractional-order PID tuning by iterative non-smooth static-dynamic H∞ synthesis
- Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity
- The rate of convergence on fractional power dissipative operator on compact manifolds
- Fractional Langevin type equations for white noise distributions
- Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
- Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
- The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
- Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
- Properties of the set of admissible “state control” pair for a class of fractional semilinear evolution control systems
