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TRANSIENT ANOMALOUS SUB-DIFFUSION ON BOUNDED DOMAINS.

Mark M Meerschaert1, Erkan Nane2, P Vellaisamy3

  • 1Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823. mcubed@stt.msu.edu URL: http://www.stt.msu.edu/~mcubed/

Proceedings of the American Mathematical Society. American Mathematical Society
|March 19, 2014
PubMed
Summary
This summary is machine-generated.

This study presents novel strong and stochastic solutions for tempered fractional diffusion equations on bounded domains. These methods advance the understanding of anomalous diffusion processes.

Keywords:
Cauchy problemFractional diffusionboundary value problemtempered stable

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Area of Science:

  • Mathematics
  • Partial Differential Equations
  • Stochastic Analysis

Background:

  • Fractional diffusion equations model anomalous transport phenomena.
  • Tempered fractional derivatives introduce a cut-off mechanism.
  • Bounded domains present unique challenges for solving PDEs.

Purpose of the Study:

  • To develop strong and stochastic solutions for the tempered fractional diffusion equation.
  • To analyze the behavior of these equations on bounded domains.
  • To provide a comprehensive mathematical framework for tempered diffusion.

Main Methods:

  • Solving the eigenvalue problem for tempered fractional derivatives.
  • Employing separation of variables and eigenfunction expansions for strong solutions.
  • Utilizing inverse subordinators for stochastic solutions.

Main Results:

  • Established strong solutions using eigenfunction expansions.
  • Developed stochastic solutions linked to inverse subordinators.
  • Successfully applied methods to bounded domains.

Conclusions:

  • The developed methods provide effective tools for analyzing tempered fractional diffusion.
  • The study offers new insights into stochastic processes governed by these equations.
  • The findings are applicable to various fields modeling anomalous diffusion.