Generalized diffusion equation with fractional derivatives within Renyi statistics

2016/06/01 by P. Kostrobij, B. Markovych, O. Viznovych +1 · 17 citations
Mathematics · Physics and Astronomy · #Anomalous diffusion #Differential Equations and Boundary Problems #Diffusion #Diffusion equation #Distribution (mathematics) #Fractional Differential Equations Solutions #Fractional calculus #Non-equilibrium thermodynamics #Operator (biology) #Probability distribution #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1063/1.4962159

published in Journal of Mathematical Physics 57(9) (American Institute of Physics) · 12 pages

arxiv created 2016/06/01 · openalex created_date 2016/06/24 · openalex publication_date 2016/09/01 · arxiv updated 2016/09/21 · openalex updated_date 2026/08/05

Abstract

By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in generalized diffusion coefficient is performed with a power distribution with the Renyi parameter q.

Citations

• The Multifractal Time and Irreversibility in Dynamic Systems
• Magnetohydrodynamics of fractal media
• Fractional Liouville and BBGKI equations
• Hyperbolic subdiffusive impedance
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Fractional Heisenberg equation