340 research outputs found

    Optimal random search, fractional dynamics and fractional calculus

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    What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the L\'evy flight is the best option to characterize this optimal problem, however, which ignores the understanding and learning abilities of the searcher agents. In the 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.Comment: 12 pages, 7 figure

    Some fundamental properties on the sampling free nabla Laplace transform

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    Discrete fractional order systems have attracted more and more attention in recent years. Nabla Laplace transform is an important tool to deal with the problem of nabla discrete fractional order systems, but there is still much room for its development. In this paper, 14 lemmas are listed to conclude the existing properties and 14 theorems are developed to describe the innovative features. On one hand, these properties make the N-transform more effective and efficient. On the other hand, they enrich the discrete fractional order system theor
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