A new truncated M-fractional derivative for air pollutant dispersion

  • A S Tankou TagneEmail author
  • J M Ema’a Ema’a
  • G H Ben-Bolie
  • D Buske
Review paper


In this paper, we study the potential of fractional derivatives to model air pollution. We introduce an M-fractional truncated derivative type for \(\alpha \)-differentiable functions that generalizes other types of fractional derivatives. We denote this new differential operator by \(_{i}D_{\mathrm{M}}^{\alpha ,\beta }\), where the parameters \(\alpha \) and \(\beta \), associated with the order of the derivative are such that \(0<\alpha <1\), \(\beta >1\) and M is the notation to indicate that the function to be derived involves the truncated function of Mittag-Leffler with a parameter. The definition of this type of truncated M-fractional derivative satisfies the properties of the integer calculation. Based on this observation, we solved these models and we compared the solutions with the data obtained from the Copenhagen experiment. Fractional derivative models work much better than the traditional Gaussian model and the computed values are in good agreement with experimental ones.


M-fractional derivative type Truncated Mittag-Leffler Air pollutant 


82.33.Tb 47.53.+n 92.60.Sz 



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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  • A S Tankou Tagne
    • 1
    • 2
    Email author
  • J M Ema’a Ema’a
    • 4
  • G H Ben-Bolie
    • 1
    • 2
  • D Buske
    • 3
  1. 1.Laboratory of Nuclear Physics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundéCameroon
  2. 2.The African Center of Excellence in Information and Communication TechnologiesUniversity of Yaounde IYaoundéCameroon
  3. 3.Laboratory of Pollutant Dispersion Modelling and Nuclear Engineering, Department of Mathematics and Statistics, Institute of Physics and MathematicsFederal University of PelotasPelotasBrasil
  4. 4.Higher Teachers’ Training CollegeUniversity of MarouaMarouaCameroon

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