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Applications of variable-order fractional operators: a review.
Sansit Patnaik1, John P Hollkamp1, Fabio Semperlotti1
1School of Mechanical Engineering, Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47907, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|March 24, 2020
Summary
Variable-order fractional calculus (VO-FC) offers new ways to model complex systems in various fields. This review introduces VO-FC analytical and computational methods for simulating physical systems.
Area of Science:
- Mathematics
- Applied Mathematics
- Physics
Background:
- Variable-order fractional operators are recent mathematical formalizations with broad applications.
- Variable-order fractional calculus (VO-FC) enables the modeling of complex real-world problems across mechanics, transport processes, control theory, and biology.
- VO-FC presents significant opportunities for simulating interdisciplinary processes.
Purpose of the Study:
- To provide a concise and comprehensive summary of progress in VO-FC analytical and computational methods.
- To serve as an introductory resource for researchers interested in VO-FC.
- To highlight the practical applications of VO-FC in scientific modeling.
Main Methods:
- Review of fundamental mathematical concepts of VO-FC.
- Summary of analytical methods developed for VO-FC.
- Overview of computational techniques for VO-FC.
Main Results:
- Demonstration of VO-FC's utility in simulating complex physical systems.
- Identification of progress in both theoretical and applied aspects of VO-FC.
- Compilation of methods applicable to diverse scientific modeling challenges.
Conclusions:
- VO-FC is a powerful tool for modeling complex phenomena.
- Continued exploration of VO-FC methods is crucial for advancing scientific modeling.
- This review serves as a foundational guide to the field of VO-FC.
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