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. © 2018 Diogenes Co., Sofia.

Mittag-Leffler function and fractional differential equations

Dattoli, G.
2018-01-01

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. © 2018 Diogenes Co., Sofia.
2018
fractional calculus;fractional Fokker-Planck equation;moments;umbral (operational) method
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12079/2029
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