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Mittag-Leffler function and fractional differential equations

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Abstract

We adopt a procedure of operational-umbral type to solve the (1 + 1)-dimensional fractional Fokker-Planck equation in which time fractional derivative of order α (0 < α < 1) is in the Riemann-Liouville sense. The technique we propose merges well documented operational methods to solve ordinary FP equation and a redefinition of the time by means of an umbral operator. We show that the proposed method allows significant progress including the handling of operator ordering.

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Authors and Affiliations

  1. H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences ul, Eljasza-Radzikowskiego 152, PL 31342, Kraków, Poland

    Katarzyna Górska & Ambra Lattanzi

  2. ENEA - Centro Ricerche Frascati, v. le E. Fermi, 45 IT 00044, Frascati, (Roma), Italy

    Giuseppe Dattoli

Authors
  1. Katarzyna Górska
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  2. Ambra Lattanzi
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  3. Giuseppe Dattoli
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Correspondence to Katarzyna Górska.

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Górska, K., Lattanzi, A. & Dattoli, G. Mittag-Leffler function and fractional differential equations. FCAA 21, 220–236 (2018). https://doi.org/10.1515/fca-2018-0014

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