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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
Summary
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.
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.
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