Crossover dynamics from superdiffusion to subdiffusion: models and solutions

DOI10.1515/fca-2020-0003zbMath1439.35519OpenAlexW3007960120MaRDI QIDQ2176135

Ralf Metzler, Emad S. Awad

Publication date: 4 May 2020

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2020-0003

zbMATH Keywords

anomalous diffusiontelegrapher's equationFox \(H\)-functionsCattaneo equationfractional dynamic equationscrossover dynamicssuperdiffusion and subdiffusion

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Mittag-Leffler functions and generalizations (33E12) Fractional partial differential equations (35R11)

Related Items

Two efficient Galerkin finite element methods for the modified anomalous subdiffusion equation ⋮ Efficient Galerkin finite element methods for a time-fractional Cattaneo equation ⋮ Closed-form multi-dimensional solutions and asymptotic behaviours for subdiffusive processes with crossovers: II. Accelerating case ⋮ Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers. I: Retarding case ⋮ Subordination and memory dependent kinetics in diffusion and relaxation phenomena ⋮ Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting ⋮ Nonlocal-In-Time Dynamics and Crossover of Diffusive Regimes

Uses Software

• OpenCourseWare

Cites Work

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• Hilfer-Prabhakar derivatives and some applications
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Solutions of the space-time fractional Cattaneo diffusion equation
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• Some aspects of fractional diffusion equations of single and distributed order
• Fox function representation of non-Debye relaxation processes
• The fundamental solutions for the fractional diffusion-wave equation
• Time-fractional telegraph equations and telegraph processes with Brownian time
• Some applications of persistent random walks and the telegrapher's equation
• Beyond monofractional kinetics
• On a constitutive equation of heat conduction with fractional derivatives of complex order
• Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law
• Analytical solutions of the space-time fractional telegraph and advection-diffusion equations
• On the time-fractional Cattaneo equation of distributed order
• Subordination in a class of generalized time-fractional diffusion-wave equations
• Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density
• Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel
• Localisation and universal fluctuations in ultraslow diffusion processes
• Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation
• Fractional diffusion and wave equations
• Time-fractional Diffusion of Distributed Order
• Natural and Modified Forms of Distributed-Order Fractional Diffusion Equations
• The fractional diffusion equation
• The generalized Cattaneo equation for the description of anomalous transport processes
• Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
• The neutral-fractional telegraph equation
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium
• Fractional equation description of an open anomalous heat conduction set-up
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Excess wing physics and nearly constant loss in glasses
• Subdiffusive and superdiffusive transport in plane steady viscous flows
• Generalized diffusion-wave equation with memory kernel
• Mittag-Leffler Functions, Related Topics and Applications
• Bernstein functions. Theory and applications
• The random walk's guide to anomalous diffusion: A fractional dynamics approach