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N-dimensional fractional diffusion equation and Green function approach: spatially dependent diffusion coefficient

E K Lenzi1, R S Mendes, J S Andrade

  • 1Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá PR, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study explores fractional diffusion equations with spatial dependencies and external forces using Green functions. The findings reveal a wide range of diffusion processes, encompassing both normal and anomalous diffusion.

Area of Science:

  • Mathematical Physics
  • Partial Differential Equations
  • Fractional Calculus

Background:

  • Fractional diffusion equations model complex transport phenomena.
  • Understanding diffusion with spatially varying coefficients and external forces is crucial.
  • Green function methods offer powerful analytical tools for such equations.

Purpose of the Study:

  • To analyze an N-dimensional fractional diffusion equation with radial symmetry.
  • To incorporate spatial dependence in the diffusion coefficient and external forces.
  • To investigate solutions under finite and semi-infinite interval boundary conditions.

Main Methods:

  • Utilizing the Green function approach for analytical solutions.
  • Applying boundary conditions on finite and then semi-infinite intervals.

Related Experiment Videos

  • Analyzing the impact of spatial diffusion coefficient dependence and external forces.

    • Main Results:

    • Derivation of solutions for the N-dimensional fractional diffusion equation.
    • Demonstration of how spatial dependence and external forces affect diffusion dynamics.
    • Obtaining a broad spectrum of diffusive behaviors, including normal and anomalous diffusion.

    Conclusions:

    • The Green function approach provides a versatile framework for solving fractional diffusion equations.
    • The model successfully captures diverse diffusion processes.
    • This work offers insights into anomalous transport phenomena and their mathematical descriptions.