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

2012/04/16 by Mirko D’Ovidio, D'Ovidio, Mirko
Mathematics · Medicine · #60J35 #60J70 #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1204.3502

openalex publication_date 2012/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider fractional directional derivatives and establish some connection\nwith stable densities. Solutions to advection equations involving fractional\ndirectional derivatives are presented and some properties investigated. In\nparticular we obtain solutions written in terms of Wright functions by\nexploiting operational rules involving the shift operator. We also consider\nfractional advection diffusion equations involving fractional powers of the\nnegative Laplace operator and directional derivatives of fractional order and\ndiscuss the probabilistic interpretations of solutions.\n

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