Semi-fractional diffusion equations

DOI10.1515/fca-2019-0021zbMath1423.35400arXiv1806.05460OpenAlexW3104203222MaRDI QIDQ2328612

Svenja Lage, Mark M. Meerschaert, Peter Becker-Kern

Publication date: 10 October 2019

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

Full work available at URL: https://arxiv.org/abs/1806.05460

zbMATH Keywords

semi-fractional derivativesemistable Lévy processGrünwald-Letnikov Type Formulalog-characteristic functionlog-periodic perturbationZolotarev fractional derivative

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Fractional processes, including fractional Brownian motion (60G22) Characteristic functions; other transforms (60E10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Fractional partial differential equations (35R11)

Related Items (3)

Exact asymptotic formulas for the heat kernels of space and time-fractional equations ⋮ On self-similar Bernstein functions and corresponding generalized fractional derivatives ⋮ Space-time duality for semi-fractional diffusions

Cites Work

• General fractional calculus, evolution equations, and renewal processes
• From continuous time random walks to the generalized diffusion equation
• Anomalous diffusion with ballistic scaling: a new fractional derivative
• A fractional diffusion equation to describe Lévy flights
• Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel
• Finite difference approximations for two-sided space-fractional partial differential equations
• General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
• A limit theorem which clarifies the ‘Petersburg Paradox'
• ON LÉVY STABLE AND SEMISTABLE DISTRIBUTIONS
• Stochastic models for fractional calculus
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
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