Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

DOI10.1016/J.PHYSA.2016.02.056zbMath1400.82135OpenAlexW2282486370MaRDI QIDQ1619512

Yingjie Liang, Richard L. Magin, Wen Chen

Publication date: 13 November 2018

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physa.2016.02.056

zbMATH Keywords

Fourier transformLaplace transformdiffusion equationfractional derivativespectral entropylong range correlation

Mathematics Subject Classification ID

Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Fractional partial differential equations (35R11)

Related Items (8)

Space-time fractional diffusion equation using a derivative with nonsingular and regular kernel ⋮ Structural derivative based on inverse Mittag-Leffler function for modeling ultraslow diffusion ⋮ Stability analysis for fractional order advection-reaction diffusion system ⋮ On almost periodic processes in impulsive fractional-order competitive systems ⋮ A stochastic model for thermal transport of nanofluid in porous media: derivation and applications ⋮ Convergence in fractional probability space and 0-1 Kolmogorov theorem ⋮ Generalized finite difference method for a class of multidimensional space-fractional diffusion equations ⋮ The Euler-Lagrange and Legendre equations for functionals involving distributed-order fractional derivatives

Uses Software

• STABLE
• quadgk
• LSD
• mlrnd
• quadva

Cites Work

• Mittag-Leffler functions and their applications
• Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative
• Fox function representation of non-Debye relaxation processes
• The fundamental solutions for the fractional diffusion-wave equation
• On \(1/f\) noise
• Information theory, approximate time dependent solutions of Boltzmann's equation and Tsallis' entropy
• Vectorized adaptive quadrature in MATLAB
• Stochastic solution of space-time fractional diffusion equations
• Wavelet analysis and synthesis of fractional Brownian motion
• Numerical calculation of stable densities and distribution functions
• The fundamental solution of the space-time fractional diffusion equation
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Fractional kinetic equations: solutions and applications
• From diffusion to anomalous diffusion: A century after Einstein’s Brownian motion
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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