Green's function of time fractional diffusion equation and its applications in fractional quantum mechanics

DOI10.1016/J.NONRWA.2007.11.024zbMath1167.35441OpenAlexW2053356441MaRDI QIDQ837697

Mingyu Xu, Shaowei Wang, Xicheng Li

Publication date: 20 August 2009

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2007.11.024

zbMATH Keywords

Green's functionSchrödinger equationfractional calculus

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Fractional derivatives and integrals (26A33) PDEs in connection with quantum mechanics (35Q40) General mathematical topics and methods in quantum theory (81Q99)

Related Items (13)

Solutions for a fractional diffusion equation with noninteger dimensions ⋮ Quantization method and Schrödinger equation of fractional time and their weak effects on Hamiltonian: phase transitions of energy and wave functions ⋮ Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative ⋮ Time fractional Schrödinger equation revisited ⋮ Fractional Schrödinger equation with noninteger dimensions ⋮ Analysis of projectile motion in view of fractional calculus ⋮ Fundamental solutions to advection-diffusion equation with time-fractional Caputo-Fabrizio derivative ⋮ Analysis and numerical simulation for a class of time fractional diffusion equation via tension spline ⋮ Improved matrix transform method for the Riesz space fractional reaction dispersion equation ⋮ Horizontal water flow in unsaturated porous media using a fractional integral method with an adaptive time step ⋮ Analysis of the two-dimensional fractional projectile motion in view of the experimental data ⋮ Sinc methods for Lévy-Schrödinger equations ⋮ Lévy-Schrödinger Equation: Their Eigenvalues and Eigenfunctions Using Sinc Methods

Cites Work

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• Fractals and quantum mechanics
• Generalized fractional Schrödinger equation with space-time fractional derivatives
• The fractional diffusion equation
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Time fractional Schrödinger equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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