Anomalous Diffusion: Models, Their Analysis, and Interpretation

DOI10.1007/978-3-0348-0417-2_3zbMath1279.60105OpenAlexW118582339MaRDI QIDQ2840588

Yu. F. Luchko

Publication date: 22 July 2013

Published in: Advances in Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0417-2_3

zbMATH Keywords

Mittag-Leffler functionmaximum principleuniqueness theoremspectral methodanomalous diffusionFourier integral transforminitial-boundary-value problemsfractional diffusion equationLaplace integral transformrandom walk models

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Brownian motion (60J65) Fractional derivatives and integrals (26A33) Maximum principles in context of PDEs (35B50) Diffusion processes (60J60) A priori estimates in context of PDEs (35B45) Mittag-Leffler functions and generalizations (33E12) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Parabolic equations and parabolic systems (35K99)

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Cites Work

• The fractional Poisson process and the inverse stable subordinator
• Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• A fractional generalization of the Poisson processes
• Boundary value problems for multi-term fractional differential equations
• Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients
• Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
• Fractional models, non-locality, and complex systems
• Some recent advances in theory and simulation of fractional diffusion processes
• Fractional Poisson processes and related planar random motions
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• An operational method for solving fractional differential equations with the Caputo derivatives
• The Wright functions as solutions of the time-fractional diffusion equation.
• Cauchy problem for fractional diffusion equations
• Fractional Cauchy problems on bounded domains
• The Cauchy problem for the diffusion-wave equation with the Caputo partial derivative
• Existence of solution for a boundary value problem of fractional order
• Maximum principle for the generalized time-fractional diffusion equation
• Fractional diffusion and wave equations
• The fundamental solution of the space-time fractional diffusion equation
• Waves and Stability in Continuous Media
• Fractional diffusion in inhomogeneous media
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
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