Relevant bibliographies by topics / Fractional Langevin Equation (FLE)

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  2. Dissertations / Theses
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Academic literature on the topic 'Fractional Langevin Equation (FLE)'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Fractional Langevin Equation (FLE)"

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Lovejoy, Shaun. "Fractional relaxation noises, motions and the fractional energy balance equation." Nonlinear Processes in Geophysics 29, no. 1 (February 25, 2022): 93–121. http://dx.doi.org/10.5194/npg-29-93-2022.

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Abstract. We consider the statistical properties of solutions of the stochastic fractional relaxation equation and its fractionally integrated extensions that are models for the Earth's energy balance. In these equations, the highest-order derivative term is fractional, and it models the energy storage processes that are scaling over a wide range. When driven stochastically, the system is a fractional Langevin equation (FLE) that has been considered in the context of random walks where it yields highly nonstationary behaviour. An important difference with the usual applications is that we instead consider the stationary solutions of the Weyl fractional relaxation equations whose domain is −∞ to t rather than 0 to t. An additional key difference is that, unlike the (usual) FLEs – where the highest-order term is of integer order and the fractional term represents a scaling damping – in the fractional relaxation equation, the fractional term is of the highest order. When its order is less than 1/2 (this is the main empirically relevant range), the solutions are noises (generalized functions) whose high-frequency limits are fractional Gaussian noises (fGn). In order to yield physical processes, they must be smoothed, and this is conveniently done by considering their integrals. Whereas the basic processes are (stationary) fractional relaxation noises (fRn), their integrals are (nonstationary) fractional relaxation motions (fRm) that generalize both fractional Brownian motion (fBm) as well as Ornstein–Uhlenbeck processes. Since these processes are Gaussian, their properties are determined by their second-order statistics; using Fourier and Laplace techniques, we analytically develop corresponding power series expansions for fRn and fRm and their fractionally integrated extensions needed to model energy storage processes. We show extensive analytic and numerical results on the autocorrelation functions, Haar fluctuations and spectra. We display sample realizations. Finally, we discuss the predictability of these processes which – due to long memories – is a past value problem, not an initial value problem (that is used for example in highly skillful monthly and seasonal temperature forecasts). We develop an analytic formula for the fRn forecast skills and compare it to fGn skill. The large-scale white noise and fGn limits are attained in a slow power law manner so that when the temporal resolution of the series is small compared to the relaxation time (of the order of a few years on the Earth), fRn and its extensions can mimic a long memory process with a range of exponents wider than possible with fGn or fBm. We discuss the implications for monthly, seasonal, and annual forecasts of the Earth's temperature as well as for projecting the temperature to 2050 and 2100.
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Eab, C. H., and S. C. Lim. "Fractional generalized Langevin equation approach to single-file diffusion." Physica A: Statistical Mechanics and its Applications 389, no. 13 (July 2010): 2510–21. http://dx.doi.org/10.1016/j.physa.2010.02.041.

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Taloni, Alessandro, and Fabio Marchesoni. "Interacting Single-File System: Fractional Langevin Formulation Versus Diffusion-Noise Approach." Biophysical Reviews and Letters 09, no. 04 (December 2014): 381–96. http://dx.doi.org/10.1142/s1793048014400050.

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We review the latest advances in the analytical modelling of single file diffusion. We focus first on the derivation of the fractional Langevin equation that describes the motion of a tagged file particle. We then propose an alternative derivation of the very same stochastic equation by starting from the diffusion-noise formalism for the time evolution of the file density. [Formula: see text] Special Issue Comments: This article presents mathematical formulations and results on the dynamics in files with applied potential, yet also general files. This article is connected to the Special Issue articles about the zig zag phenomenon,72 advanced statistical properties in single file dynamics,73 and expanding files.74
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Lim, S. C., and L. P. Teo. "Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 08 (August 13, 2009): P08015. http://dx.doi.org/10.1088/1742-5468/2009/08/p08015.

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Taloni, Alessandro. "Kubo Fluctuation Relations in the Generalized Elastic Model." Advances in Mathematical Physics 2016 (2016): 1–16. http://dx.doi.org/10.1155/2016/7502472.

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The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. In this paper we show that the Fractional Langevin Equation (FLE) is a suitable framework for the study of the tracer (probe) particle dynamics, when an external force actsonlyon a single pointx→⋆(tagged probe) belonging to the system. With the help of the Fox function formalism we study the scaling behaviour of the noise- and force-propagators for large and short times (distances). We show that the Kubo fluctuation relations are exactly fulfilled when a time periodic force is exerted on the tagged probe. Most importantly, by studying the large and low frequency behaviour of the complex mobility we illustrate surprising nontrivial physical scenarios. Our analysis shows that the system splits into two distinct regions whose size depends on the applied frequency, characterized by very different response to the periodic perturbation exerted, both in the phase shift and in the amplitude.
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Qiu, Lini, Guitian He, Yun Peng, Hui Cheng, and Yujie Tang. "Noise Spectral of GML Noise and GSR Behaviors for FGLE with Random Mass and Random Frequency." Fractal and Fractional 7, no. 2 (February 10, 2023): 177. http://dx.doi.org/10.3390/fractalfract7020177.

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Due to the interest of anomalous diffusion phenomena and their application, our work has widely studied a fractional-order generalized Langevin Equation (FGLE) with a generalized Mittag–Leffler (GML) noise. Significantly, the spectral of GML noise involving three parameters is well addressed. Furthermore, the spectral amplification (SPA) of an FGLE has also been investigated. The generalized stochastic resonance (GSR) phenomenon for FGLE only influenced by GML noise has been found. Furthermore, material GSR for FGLE influenced by two types of noise has been studied. Moreover, it is found that the GSR behaviors of the FGLE could also be induced by the fractional orders of the FGLE.
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DEVI, AMITA, ANOOP KUMAR, THABET ABDELJAWAD, and AZIZ KHAN. "EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS." Fractals 28, no. 08 (June 25, 2020): 2040006. http://dx.doi.org/10.1142/s0218348x2040006x.

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In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.
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Barakat, Mohamed A., Abd-Allah Hyder, and Doaa Rizk. "New fractional results for Langevin equations through extensive fractional operators." AIMS Mathematics 8, no. 3 (2022): 6119–35. http://dx.doi.org/10.3934/math.2023309.

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<abstract><p>Fractional Langevin equations play an important role in describing a wide range of physical processes. For instance, they have been used to describe single-file predominance and the behavior of unshackled particles propelled by internal sounds. This article investigates fractional Langevin equations incorporating recent extensive fractional operators of different orders. Nonperiodic and nonlocal integral boundary conditions are assumed for the model. The Hyres-Ulam stability, existence, and uniqueness of the solution are defined and analyzed for the suggested equations. Also, we utilize Banach contraction principle and Krasnoselskii fixed point theorem to accomplish our results. Moreover, it will be apparent that the findings of this study include various previously obtained results as exceptional cases.</p></abstract>
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Zhang, Binlin, Rafia Majeed, and Mehboob Alam. "On Fractional Langevin Equations with Stieltjes Integral Conditions." Mathematics 10, no. 20 (October 19, 2022): 3877. http://dx.doi.org/10.3390/math10203877.

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In this paper, we focus on the study of the implicit FDE involving Stieltjes integral boundary conditions. We first exploit some sufficient conditions to guarantee the existence and uniqueness of solutions for the above problems based on the Banach contraction principle and Schaefer’s fixed point theorem. Then, we present different kinds of stability such as UHS, GUHS, UHRS, and GUHRS by employing the classical techniques. In the end, the main results are demonstrated by two examples.
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Ahmad, Bashir, and Juan J. Nieto. "Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions." International Journal of Differential Equations 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/649486.

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We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
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Dissertations / Theses on the topic "Fractional Langevin Equation (FLE)"

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Sposini, Vittoria. "A numerical study of fractional diffusion through a Langevin approach in random media." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12494/.

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The study of Brownian motion has a long history and involves many different formulations. All these formulations show two fundamental common results: the mean square displacement of a diffusing particle scales linearly with time and the probability density function is a Guassian distribution. However standard diffusion is not universal. In literature there are numerous experimental measurements showing non linear diffusion in many fields including physics, biology, chemistry, engineering, astrophysics and others. This behavior can have different physical origins and has been found to occur frequently in spatially disordered systems, in turbulent fluids and plasmas, and in biological media with traps, binding sites or macro-molecular crowding. Langevin approach describes the Brownian motion in terms of a stochastic differential equation. The process of diffusion is driven by two physical parameters, the relaxation or correlation time tau and the velocity diffusivity coefficient Dv. An extension of the classical Langevin approach by means of a population of tau and Dv is here considered to generate a fractional dynamics. This approach supports the idea that fractional diffusion in complex media results from Gaussian processes with random parameters, whose randomness is due to the medium complexity. A statistical characterization of the complex medium in which the diffusion occurs is realized deriving the distributions of these parameters. Specific populations of tau and Dv lead to particular fractional diffusion processes. This approach allows for preserving the classical Brownian motion as basis and it is promising to formulate stochastic processes for biological systems that show complex dynamics characterized by fractional diffusion. A numerical study of this new alternative approach represents the core of the present thesis.
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Book chapters on the topic "Fractional Langevin Equation (FLE)"

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Sandev, Trifce, and Živorad Tomovski. "Generalized Langevin Equation." In Fractional Equations and Models, 247–300. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29614-8_6.

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Sandev, Trifce, and Živorad Tomovski. "Fractional Generalized Langevin Equation." In Fractional Equations and Models, 301–35. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29614-8_7.

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Cooke, Jennie. "A Fractional Langevin Equation Approach to Diffusion Magnetic Resonance Imaging." In Advances in Chemical Physics, 279–378. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118135242.ch5.

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Ahmad, Bashir, Ahmed Alsaedi, Sotiris K. Ntouyas, and Jessada Tariboon. "Nonlinear Langevin Equation and Inclusions Involving Hadamard-Caputo Type Fractional Derivatives." In Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, 209–61. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52141-1_7.

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Rangaig, Norodin A., Alvanh Alem G. Pido, and Caironesa P. Dulpina. "Solution of Fractional Langevin Equation with Exponential Kernel and Its Anomalous Relaxation Function." In Applications of Fractional Calculus to Modeling in Dynamics and Chaos, 475–86. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003006244-19.

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Lutz, Eric. "Fractional Langevin Equation." In Fractional Dynamics, 285–305. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814340595_0012.

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"Fractional Langevin Equation." In Studies of Nonlinear Phenomena in Life Science, 393–99. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812815361_0039.

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Conference papers on the topic "Fractional Langevin Equation (FLE)"

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Metzler, Ralf. "From the Langevin equation to the fractional Fokker–Planck equation." In Stochastic and chaotic dynamics in the lakes. AIP, 2000. http://dx.doi.org/10.1063/1.1302409.

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Zeng, Xiaolong, Yanchun Zhao, and Fusheng Li. "A numerical solution method for over-damped fractional Langevin equation based on predictive correction approach." In 2020 International Conference on Intelligent Computing, Automation and Systems (ICICAS). IEEE, 2020. http://dx.doi.org/10.1109/icicas51530.2020.00078.

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Devi, Amita, and Anoop Kumar. "Existence of solutions for fractional Langevin equation involving generalized Caputo derivative with periodic boundary conditions." In ADVANCEMENTS IN MATHEMATICS AND ITS EMERGING AREAS. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0003365.

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Journal articles
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