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Fractional Approach for Estimating Sap Velocity in Trees

AuthorsTejado, Inés; Vinagre, Blas M.; Torres, Daniel; López-Bernal, Álvaro ; Villalobos, Francisco J. ; Testi, Luca ; Podlubny, Igor
Mittag-Leffler function
Issue Date2015
PublisherWalter de Gruyter
CitationFractional Calculus and Applied Analysis 18(2): 479-494 (2015)
AbstractIn the context of fractional calculus (FC), this paper is devoted to model thermal processes in trees based on the measurement of the temperature difference (ΔT) between sensors located above and below a heater inserted in the tree trunk. By evaluating several temperature curves taken from real trees of different species, the current approach shows that the temperature in each probe can be successfully described by the two-parameter Mittag- Leffler function Eα,β. Then, a simple methodology is followed to derive a novel expression of the heat-pulse velocity (v) as a function of ΔT and the parameter α of the mentioned Eα,β function. Experimental results are given to validate the goodness of the current proposal.
Publisher version (URL)http://doi.org/10.1515/fca-2015-0030
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