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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
Summary
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.
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.
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