Analytic approaches of the anomalous diffusion: a review
From MaRDI portal
Publication:2213089
DOI10.1016/j.chaos.2019.04.039zbMath1448.60193arXiv1905.02568OpenAlexW2944424549WikidataQ127921361 ScholiaQ127921361MaRDI QIDQ2213089
Publication date: 27 November 2020
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.02568
Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Research exposition (monographs, survey articles) pertaining to probability theory (60-02) Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) (60K50)
Related Items
Mittag-Leffler functions in superstatistics ⋮ Random diffusivity models for scaled Brownian motion ⋮ Anomalous diffusion originated by two Markovian hopping-trap mechanisms ⋮ Anomalous diffusion: fractional Brownian motion vs fractional Ito motion ⋮ Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion ⋮ Random diffusivity scenarios behind anomalous non-Gaussian diffusion ⋮ Efficient approach to time-dependent super-diffusive Lévy random walks on finite 2D-tori using circulant analogues ⋮ Superstatistical approach of the anomalous exponent for scaled Brownian motion ⋮ Power Brownian motion ⋮ Structure-preserving discretization of fractional vector calculus using discrete exterior calculus ⋮ Hydrodynamic fluctuations in the presence of one parameter Mittag-Leffler friction ⋮ Monitoring Lévy-process crossovers ⋮ Spectral analysis of fractional hyperbolic diffusion equations with random data ⋮ A note on Euler method for the overdamped generalized Langevin equation with fractional noise ⋮ Nonlocal pattern formation effects in evolutionary population dynamics ⋮ Equilibrium and non-equilibrium statistical mechanics with generalized fractal derivatives: A review ⋮ Collective topological active particles: non-ergodic superdiffusion and ageing in complex environments
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hilfer-Prabhakar derivatives and some applications
- Comb-like models for transport along spiny dendrites
- Solutions of some nonlinear diffusion equations and generalized entropy framework
- Computing the non-linear anomalous diffusion equation from first principles
- Dynamics of normal and anomalous diffusion in nonlinear Fokker-Planck equations
- \(q\)-Gaussians in the porous-medium equation: stability and time evolution
- Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
- A nonextensive approach to the dynamics of financial observables
- Computational applications of nonextensive statistical mechanics
- Weakly non-ergodic statistical physics
- On a \(q\) -central limit theorem consistent with nonextensive statistical mechanics
- Fox function representation of non-Debye relaxation processes
- \(q\)-exponential, Weibull, and \(q\)-Weibull distributions: An empirical analysis
- Invariance principles for tempered fractionally integrated processes
- Generalized Langevin equation with tempered memory kernel
- From continuous time random walks to the generalized diffusion equation
- Time-space fractional derivative models for \(\text{CO}_{2}\) transport in heterogeneous media
- Generalized Langevin equation and the Prabhakar derivative
- Nonextensive kinetic theory and \(H\)-theorem in general relativity
- Tempered fractional Brownian and stable motions of second kind
- On the analysis of fractional diabetes model with exponential law
- A generalization of the Mittag-Leffler function and solution of system of fractional differential equations
- The extended fractional Caputo-Fabrizio derivative of order \(0\leq \sigma <1\) on \(C_{\mathbb{R}}[0,1\) and the existence of solutions for two higher-order series-type differential equations]
- New aspects of Opial-type integral inequalities
- Moderate deviations for the Langevin equation with strong damping
- Anomalous diffusion with an irreversible linear reaction and sorption-desorption process
- The Fokker-Planck equation. Methods of solutions and applications.
- Financial market dynamics
- Possible generalization of Boltzmann-Gibbs statistics.
- Solving PDEs of fractional order using the unified transform method
- On high order fractional integro-differential equations including the Caputo-Fabrizio derivative
- A new fractional operator of variable order: application in the description of anomalous diffusion
- Thermodynamic framework for compact \(q\)-Gaussian distributions
- A time fractional convection-diffusion equation to model gas transport through heterogeneous soil and gas reservoirs
- Non validity of index law in fractional calculus: a fractional differential operator with Markovian and non-Markovian properties
- New numerical method and application to Keller-Segel model with fractional order derivative
- Fractional calculus via Laplace transform and its application in relaxation processes
- A new collection of real world applications of fractional calculus in science and engineering
- Approach of complexity in nature: entropic nonuniqueness
- Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: analytical solution in bounded-domain and model comparison
- Subordination in a class of generalized time-fractional diffusion-wave equations
- High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: construction and application (I)
- Nonlinear Fokker-Planck equations. Fundamentals and applications.
- Fractional Brownian motion as a weak limit of Poisson shot noise processes -- with applications to finance
- Superstatistics: theory and applications
- Random Walks on Lattices. II
- Fractional diffusion and wave equations
- Aging and nonergodicity beyond the Khinchin theorem
- A fractional Fokker–Planck equation for non-singular kernel operators
- Anomalous Diffusion Arising from Microinstabilities in a Plasma
- Asymptotic Analysis of Nonlinear Marshak Waves
- Viscous sheets advancing over dry beds
- Foundations of Complex-system Theories
- The fundamental solution of the space-time fractional diffusion equation
- A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian
- Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative
- Retracted: New two step Laplace Adam‐Bashforth method for integer a noninteger order partial differential equations
- Analytical solutions of Hristov diffusion equations with non-singular fractional derivatives
- Boundary Problems for the Fractional and Tempered Fractional Operators
- Fractional kinetic equations: solutions and applications
- Langevin equation in systems with also negative temperatures
- Transport, Collective Motion, and Brownian Motion
- Time dependent solutions for a fractional Schrödinger equation with delta potentials
- Fractional Brownian Motions, Fractional Noises and Applications
- Anomalous Diffusion of a Plasma across a Magnetic Field
- Superstatistics
- Renormalization group approach to nonextensive statistical mechanics
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
