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Telegraphic Transport Processes and Their Fractional Generalization: A Review and Some Extensions.

Jaume Masoliver1

  • 1Department of Condensed Matter Physics and Complex Systems Institute (UBICS), University of Barcelona, 08007 Barcelona, Catalonia, Spain.

Entropy (Basel, Switzerland)
|April 3, 2021
PubMed
Summary
This summary is machine-generated.

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This study explores telegraphic transport in multiple dimensions, reviewing fractional telegrapher's equations derived from random walk models. New solutions for higher-dimensional fractional equations are presented, advancing transport phenomena understanding.

Area of Science:

  • Physics
  • Applied Mathematics
  • Physical Chemistry

Background:

  • Telegraphic transport describes wave propagation with losses.
  • Understanding transport phenomena is crucial in various scientific fields.
  • Fractional calculus offers advanced modeling capabilities for complex systems.

Purpose of the Study:

  • To review the derivation of multi-dimensional telegrapher's equations and their fractional generalizations.
  • To explore the connection between microscopic random walk models and macroscopic transport equations.
  • To present novel solutions for higher-dimensional fractional telegrapher's equations.

Main Methods:

  • Derivation of telegrapher's equations from random walk models (normal and anomalous).
  • Generalization of these equations to fractional calculus in two and three dimensions.
Keywords:
continuous time random walkfractional telegrapher’s equationtelegrapher’s equationstransport problems

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  • Analytical and/or numerical methods for solving higher-dimensional fractional equations.

    • Main Results:

    • Established a framework for telegraphic transport in multiple dimensions.
    • Demonstrated the utility of fractional calculus in modeling anomalous transport.
    • Provided new solutions for complex, higher-dimensional fractional transport equations.

    Conclusions:

    • Fractional telegrapher's equations provide a powerful tool for describing anomalous transport phenomena.
    • The random walk model provides a fundamental basis for telegraphic transport equations.
    • This work contributes to the mathematical and physical understanding of transport processes.