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Fractional Calculus and Applied Analysis

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Volume 17, Issue 2


Optimal random search, fractional dynamics and fractional calculus

Caibin Zeng
  • School of Sciences and School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China
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/ YangQuan Chen
  • Mechatronics, Embedded Systems and Automation (MESA) Lab School of Engineering, University of California, Merced, 5200 North Lake Road, Merced, CA, 95343, USA
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Published Online: 2014-03-21 | DOI: https://doi.org/10.2478/s13540-014-0171-7


What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the Lévy flight is the best option to characterize this optimal problem, however, which ignores the understanding and learning abilities of the searcher agents. In this paper we propose the Continuous Time Random Walk (CTRW) optimal search framework and find the optimum for both of search length’s and waiting time’s distributions. Based on fractional calculus technique, we further derive its master equation to show the mechanism of such complex fractional dynamics. Numerous simulations are provided to illustrate the non-destructive and destructive cases.

MSC: Primary 26A33; Secondary 82b41, 34A08, 49Kxx

Keywords: random search; fractional dynamics; continuous time random work; fractional calculus; Lévy flight

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About the article

Published Online: 2014-03-21

Published in Print: 2014-06-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 17, Issue 2, Pages 321–332, ISSN (Online) 1314-2224, DOI: https://doi.org/10.2478/s13540-014-0171-7.

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© 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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