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Fractional Approach for Estimating Sap Velocity in Trees

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Abstract

In the context of fractional calculus (FC), this paper is devoted to model thermal processes in trees based on the measurement of the temperature difference (?T) 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 Ea,ß. Then, a simple methodology is followed to derive a novel expression of the heat-pulse velocity (v) as a function of ?T and the parameter a of the mentioned Ea,ß function. Experimental results are given to validate the goodness of the current proposal.

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Authors and Affiliations

  1. Industrial Engineering School, University of Extremadura, 06006, Badajoz, Spain

    Inés Tejado, Blas M. Vinagre & Daniel Torres

  2. Instituto de Agricultura Sostenible (IAS) - CSIC, 14080, Córdoba, Spain

    Álvaro López-Bernal, Francisco J. Villalobos & Luca Testi

  3. Dept. Agronomía, Universidad de Córdoba, 14080, Córdoba, Spain

    Francisco J. Villalobos & Luca Testi

  4. Faculty of BERG, Technical University of Kosice, 14080, Kosice, Slovakia

    Igor Podlubny

Authors
  1. Inés Tejado
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  2. Blas M. Vinagre
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  3. Daniel Torres
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  4. Álvaro López-Bernal
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  5. Francisco J. Villalobos
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  6. Luca Testi
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  7. Igor Podlubny
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Correspondence to Inés Tejado.

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Tejado, I., Vinagre, B.M., Torres, D. et al. Fractional Approach for Estimating Sap Velocity in Trees. FCAA 18, 479–494 (2015). https://doi.org/10.1515/fca-2015-0030

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  • DOI: https://doi.org/10.1515/fca-2015-0030

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