Fractional Langevin equation [PDF]
Physical Review E, 2001 We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath.
A. Caspi +37 more
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Fractional Langevin Equation of Distributed Order [PDF]
Physical Review E, 2010 Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent.
Eab, C. H., Lim, S. C.
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Axioms, 2022 The fractional Langevin equation has more advantages than its classical equation in representing the random motion of Brownian particles in complex viscoelastic fluid.
Kaihong Zhao
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Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes [PDF]
Entropy, 2018 The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and
Johan Anderson, Sara Moradi, Tariq Rafiq
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q-Fractional Langevin Differential Equation with q-Fractional Integral Conditions
Mathematics, 2023 The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q-fractional Langevin differential equation with q-fractional integral conditions.
Wuyang Wang +4 more
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Existence of Solutions to Nonlinear Langevin Equation Involving Two Fractional Orders with Boundary Value Conditions [PDF]
Boundary Value Problems, 2011 We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.
Chen Yi, Chen Anping
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Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach [PDF]
Physical Review E, 2012 The Generalized Elastic Model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, growing interfaces.
A. L. Barabasi +15 more
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Existence of solution for fractional Langevin equation: Variational approach [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We consider the Dirichlet problem for the fractional Langevin equation with two fractional order derivatives \begin{align*} -{_{0}}D_{t}^{\alpha}(_{0}D_{t}^{\alpha}u(t)) &= f(t,u(t), {_{0}}D_{t}^{\alpha}u(t)), \quad t\in [0,1],\\ u(0) &= u(1) = 0 ...
César Torres Ledesma
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Langevin Equations with Generalized Proportional Hadamard-Caputo Fractional Derivative. [PDF]
Comput Intell Neurosci, 2021 We look at fractional Langevin equations (FLEs) with generalized proportional Hadamard–Caputo derivative of different orders. Moreover, nonlocal integrals and nonperiodic boundary conditions are considered in this paper. For the proposed equations, the Hyres–Ulam (HU) stability, existence, and uniqueness (EU) of the solution are defined and ...
Barakat MA +3 more
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Multi-Strip and Multi-Point Boundary Conditions for Fractional Langevin Equation
Fractal and Fractional, 2020 In the present paper, we discuss a new boundary value problem for the nonlinear Langevin equation involving two distinct fractional derivative orders with multi-point and multi-nonlocal integral conditions.
Ahmed Salem, Balqees Alghamdi
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