English

Fractional gradient and its application to the fractional advection equation

Mathematical Physics 2013-05-21 v1 math.MP Probability

Abstract

In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\'evy processes.

Keywords

Cite

@article{arxiv.1305.4400,
  title  = {Fractional gradient and its application to the fractional advection equation},
  author = {M. D'Ovidio and R. Garra},
  journal= {arXiv preprint arXiv:1305.4400},
  year   = {2013}
}