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INVERSE STABLE SUBORDINATORS.

Mark M Meerschaert1, Peter Straka2

  • 1Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824.

Mathematical Modelling of Natural Phenomena
|July 22, 2014
PubMed
Summary
This summary is machine-generated.

The inverse stable subordinator offers a probability model for time-fractional differential equations, yielding explicit solutions. This review reconciles various proposed governing equations for this subordinator, highlighting its mathematical and physical applications.

Keywords:
fractional derivativegoverning equationhitting timesubordinator

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Area of Science:

  • Mathematics
  • Physics
  • Probability Theory

Background:

  • The inverse stable subordinator is a key probability model.
  • It is crucial for solving time-fractional differential equations.
  • Explicit solution formulas are derived from this model.

Purpose of the Study:

  • To review the properties of the inverse stable subordinator.
  • To explore its applications in mathematics and physics.
  • To reconcile different governing equations for the inverse stable subordinator.

Main Methods:

  • Literature review of the inverse stable subordinator.
  • Analysis of its properties and applications.
  • Comparison and reconciliation of proposed governing equations.

Main Results:

  • Comprehensive overview of inverse stable subordinator properties.
  • Demonstration of its utility in diverse mathematical and physical problems.
  • A unified approach to previously disparate governing equations.

Conclusions:

  • The inverse stable subordinator is a versatile tool.
  • Reconciliation of governing equations simplifies its study.
  • Further applications in fractional calculus and applied sciences are expected.