Methods and Applications of Analysis

Volume 22 (2015)

Number 1

Wright functions governed by fractional directional derivatives and fractional advection diffusion equations

Pages: 1 – 36



Mirko D’Ovidio (Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza University of Rome, Italy)


We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular we obtain solutions written in terms of Wright functions by exploiting operational rules involving the shift operator. We also consider fractional advection diffusion equations involving fractional powers of the negative Laplace operator and directional derivatives of fractional order and discuss the probabilistic interpretations of solutions.


directional derivative, Wright function, stable subordinator, fractional diffusion, advection equation, translation operator

2010 Mathematics Subject Classification

35R11, 60J35, 60J70

Published 1 April 2015